Matematika · DTM

Hisoblang: \((1 - \frac{1}{7}) \cdot (1 - \frac{1}{8}) \cdot (1 - \frac{1}{9}) \cdot \dots \cdot (1 - \frac{1}{62})\)

Hisoblang: \(\frac{1}{2} + \frac{2}{3} + \frac{3}{2} + \frac{4}{3} + \dots + \frac{15}{2} + \frac{16}{3}\)

Agar \(a = 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \dots + 40 \cdot 41\) va \(b = 5 \cdot 4 + 10 \cdot 6 + 15 \cdot 8 + \dots + 200 \cdot 82\) bo'lsa, \(\frac{a}{b}\) ning qiymatini toping.

Hisoblang: \((1 - \frac{1}{7}) \cdot (1 - \frac{1}{8}) \cdot (1 - \frac{1}{9}) \cdot \dots \cdot (1 - \frac{1}{69})\)

Hisoblang: \(\frac{2}{1^2 \cdot 2^2} + \frac{3}{2^2 \cdot 3^2} + \frac{4}{3^2 \cdot 4^2} + \dots + \frac{39}{19^2 \cdot 20^2}\)

Agar \(a = 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \dots + 42 \cdot 43\) va \(b = 5 \cdot 4 + 10 \cdot 6 + 15 \cdot 8 + \dots + 210 \cdot 86\) bo'lsa, \(\frac{b}{a}\) ning qiymatini toping.

Hisoblang: \(\frac{1 \cdot 2 \cdot 3 + 3 \cdot 6 \cdot 9 + 5 \cdot 10 \cdot 15 + 7 \cdot 14 \cdot 21}{2 \cdot 4 \cdot 6 + 6 \cdot 12 \cdot 18 + 10 \cdot 20 \cdot 30 + 14 \cdot 28 \cdot 42}\)

Hisoblang: \(1 - 2 + 3 - 4 + 5 - 6 + \dots + 195 - 196\)

Hisoblang: \(-2019 + 2019 - 2019 + \dots + 2019 - 2019\) (2019 ta)

2: 3 sonidan 1: 2: 3 soni nechaga katta?

2019^{5/26} - 2017^{2/13} ni hisoblang.

(4/3^{8} - 1/3^{4}) : 1/3^{4} ni hisoblang.

Quyida berilgan sonlardan eng kattasini toping.

Hisoblang: (2020^{7/8} - 2019^{3/8}) : (2019^{1/3} - 2018^{5/6})

Hisoblang: 333 + 222 + 333

Hisoblang: \(1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{5}}}\)

Hisoblang: \(\frac{7}{8} + \frac{7}{8} - 1 + \frac{1}{2}\)

Hisoblang: \((2018 - \frac{1}{2018}) : (1 - \frac{1}{2018})\)

n natural sonning qanday qiymatida \(\frac{2 + \frac{1}{1+2}}{n} = \frac{13}{5}\) tenglik o'rinli bo'ladi?

m ning qanday qiymatida \(\frac{9m+7}{6}\) ifodaning qiymati \(11\frac{2}{3}\) ga teng bo'ladi?

Agar 𝑛 va 𝑚 natural sonlar uchun 6𝑛−4𝑚 𝑛 = 1 tenglik bajarilsa, 1 𝑛 + 2 𝑚 ifodaning eng katta qiymatini toping.

3/4 + 34/44 + 334/444 + 3334/4444 yig'indining qiymati qaysi oraliqda yotadi?

27/13 + 77/19 - 70/23 sonli ifodaning qiymati quyidagi oraliqlardan qaysi birida yotadi?

Agar 𝑎 va 𝑏 ratsional sonlar uchun 𝑎+ 𝑏⋅√3 3 = 3 bo'lsa, u holda 𝑎^2 + 𝑏^2 ifodaning qiymatini toping.

𝑎, 𝑏, 𝑐 sonlar uchun \(7a=2b=3c\) va \(\frac{a}{3} - \frac{5b}{2} + \frac{2c}{5} = 3\frac{2}{5}\) tengliklar o'rinli bo'lsa, \(\frac{b}{c-a}\) ning qiymatini toping.

1/3 va 5/6 sonlar orasida maxraji 24 bo'lgan, qisqarmaydigan barcha kasrlar yig'indisini toping.

Hisoblang: \((\frac{7}{17} - \frac{9}{36}) : \frac{2}{9} - \frac{3}{26} \cdot 4\frac{1}{3} + 3\)

Hisoblang: \(1\frac{1}{2} \cdot 3\frac{3}{5} + 2\frac{3}{4} \cdot 3\frac{3}{5} - 3\frac{3}{5} \cdot 3\frac{5}{6} - 1\frac{1}{2}\)

Hisoblang: \( (6 \frac{5}{12} - 3 \frac{3}{4}) : 1 \frac{7}{9} \)

Quyida berilgan sonlardan eng kattasini toping.

Hisoblang: \( 1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{6}}} \)

Hisoblang: \( (2019 - \frac{1}{2019}) : (1 - \frac{1}{2019}) \)

\(n\) natural sonning qanday qiymatida \( 2 + \frac{1}{n+2} = \frac{13}{5} \) tenglik o'rinli bo'ladi?

\(a=\frac{2}{23}\), \(b=\frac{3}{24}\) va \(c=\frac{4}{25}\) sonlarni taqqoslang.

Hisoblang: \( 1 + (1 - \frac{1}{2}) \)

Hisoblang: $$ \left(1 - \frac{1}{2}\right) \cdot \left(1 - \frac{1}{3}\right) \cdot \left(1 - \frac{1}{4}\right) \cdot \left(1 - \frac{1}{5}\right) \cdot \left(1 - \frac{1}{6}\right) $$

Agar \(a\) va \(b\) natural sonlar bo'lsa, \(a + \frac{b}{4} = 10\) tenglik o'rinli bo'lsa, \(ab\) ifodaning eng katta qiymatini toping.

Quyidagi ifodaning qiymati qaysi oraliqda yotadi? $$ \frac{2}{4} + \frac{23}{44} + \frac{223}{444} + \frac{2223}{4444} $$

Quyidagi ifodaning qiymati qaysi oraliqlardan qaysi birida yotadi? $$ \frac{27}{13} + \frac{77}{19} - \frac{93}{23} $$

Agar \(n\) natural son uchun \(\frac{n^2-n+2}{n+1}\) kasrning qiymati \((1; 2)\) oralig'ida joylashgan bo'lsa, kasrning shu oraliqdagi qiymatini toping.

Agar \(a\) va \(b\) natural sonlar uchun \(\frac{a}{5} = \frac{9}{b+3}\) bo'lsa, u holda \(a+b\) ifodaning eng katta qiymatini toping.

Agar \(a = \frac{210+1}{211+1}\) va \(b = \frac{211+1}{212+1}\) sonlar uchun quyidagi munosabatlardan qaysi biri to'g'ri?

Agar \(\frac{27}{38} + \frac{49}{57} + \frac{19}{43} = a\) bo'lsa, \(\frac{65}{38} - \frac{8}{57} + \frac{62}{43}\) quyidagilardan qaysi biriga teng?

Hisoblang: \(1 \div \frac{2}{3} \div \frac{4}{5} + \frac{1}{2} \div \frac{3}{4}\)

\(a\) va \(b\) ratsional sonlar. Agar \(a - \sqrt{5} \cdot b = 5\) tenglik o'rinli bo'lsa, \(a^2 + b^2\) ni toping.

Hisoblang: \(\frac{3}{4} \div \frac{5}{6} + 2\frac{1}{2} \cdot \frac{2}{5} - 1 \div 1\frac{1}{9}\)

Hisoblang: \(28 \cdot \left(\frac{7}{5} : \frac{3}{5} - \frac{1}{7}\right) + \frac{5}{6} : \left(\frac{5}{12} - \frac{1}{14}\right)\)

Hisoblang: \(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}\)

Hisoblang: \(\frac{1}{2} - \frac{1}{3} + \frac{1}{6}\)

Hisoblang: \(\frac{4}{5} : \left(-2\frac{5}{8}\right) : \frac{2}{3} : \left(-1\frac{3}{7}\right) : \frac{2}{5}\)

Hisoblang: \(\frac{3}{4} : \left(-1\frac{3}{5}\right) : \frac{6}{7} : \left(-2\frac{1}{3}\right) : \frac{3}{16}\)

Maxraji 20 ga teng va \(\frac{1}{2}\) va \(\frac{3}{4}\) orasida yotuvchi qisqarmas kasrlar yig'indisini toping.

Hisoblang: \(\frac{1}{6} - \frac{1}{3}\)

Hisoblang: \((\frac{5}{6} - \frac{1}{3}) (\frac{1}{6} - \frac{2}{3})\)

Hisoblang: \(\frac{5}{26} - \frac{2}{13}\)

Hisoblang: \(1: 4 \cdot 2 - \frac{1}{3}\)

Hisoblang: \(1: 3 \cdot 4 - 1: 3\)

Hisoblang: \(\frac{9}{19} \cdot (\frac{2}{9} + \frac{1}{5})\)

-7 dan 9 gacha nechta butun son bor.

Hisoblang: \( \frac{1}{2} - \frac{1}{2} \times \frac{2}{3} \)

Hisoblang: \(-5 + (\frac{3}{5} \times \frac{1}{3})\)

-7 dan 9 gacha nechta natural son bor.

[−10; 6] oralig'idagi eng katta butun manfiy son bilan eng katta butun musbat sonlarni yigindisini toping.

𝑎 va 𝑏 ratsional sonlar uchun \(a + 2\sqrt{2}b = 12\) bolsa, \(a + b\) ning qiymatini toping.

Quyidagilarni orasidan eng katta sonni toping: \(a=\frac{5}{8}\) ; \(b=\frac{23}{36}\) ; \(c=\frac{47}{72}\) ; \(d=\frac{7}{12}\).

Hisoblang: \((-13)^2 + 14 \cdot (-12)\)

Ifodaning qiymati qaysi oraliqda yotadi: \(\frac{1}{2} - \frac{5}{11} + \frac{55}{111} - \frac{555}{1111}\).

Ifodaning qiymati qaysi oraliqda yotadi: \(\frac{5}{8} + \frac{45}{88} + \frac{445}{888} - \frac{4445}{8888}\).

Ifodaning qiymati qaysi oraliqda bo'ladi: \(\frac{52}{17} + \frac{39}{19} - \frac{85}{21}\).

Hisoblang: \(\frac{5}{6} : \frac{15}{24} + \frac{1}{2} : \frac{1}{4}\).

Hisoblang: \(3\frac{1}{2} \cdot 2\frac{2}{5}\).

Hisoblang: \(\frac{1}{5} \cdot \frac{3}{8}\)

Hisoblang: \(\frac{3}{5} : \frac{1}{9}\)

Son o'qida M(-12) nuqtani necha birlik va qaysi tomonga siljitsak N(-7) nuqtaga boradi?

Ifodaning qiymati qaysi oraliqda yotadi: \(\frac{2}{3} + \frac{23}{33} + \frac{223}{333} + \frac{2223}{3333}\)

1/7 soni 1/8 sonidan qanchaga ko’p?

Ifodaning qiymati qaysi oraliqda yotadi: \(\frac{2}{3} + \frac{23}{33} - \frac{223}{333} + \frac{2223}{3333} - \frac{22223}{33333}\)

Ifodaning qiymati qaysi oraliqda yotadi: $$ \frac{2}{3} + \frac{23}{33} + \frac{223}{333} + \frac{2223}{3333} + \frac{22223}{33333} $$

Hisoblang: $$ \frac{2}{5} - 1 \frac{1}{3} $$

Hisoblang: $$ \frac{3}{2} \times \frac{3}{5} + 2 \times \frac{1}{10} $$

Hisoblang: $$ \left( \frac{2022^2 - 1}{2022} \right) : \frac{2021}{2022} \times \frac{1}{2023} $$

Hisoblang: $$ \frac{1-3+5-7+9-11+\dots+2021-2023}{1-2+3-4+5-6+\dots+2021-2022} $$

Hisoblang: $$ \frac{18}{65} \times \left( \frac{41}{18} - \frac{17}{36} \right) + \frac{7}{6} + \left( \frac{8}{7} - \frac{23}{49} \right) : \frac{99}{49} $$

Hisoblang: \(\frac{1}{30} + \frac{1}{60} + \frac{1}{100} + \frac{1}{150} + \frac{1}{210}\)

Hisoblang: \(6 - \frac{31}{30} - \frac{61}{60} - \frac{101}{100} - \frac{151}{150} - \frac{211}{210}\)

Agar \(x = 1 + 4 + 7 + \dots + 301\) va \(y = 2 + 8 + 14 + \dots + 602\) bo'lsa, \(\frac{y+2022x}{x}\) ni hisoblang.

Hisoblang: \(\frac{4 - \frac{1}{3} + \frac{1}{4}}{4 + \frac{1}{3} - \frac{1}{4}}\)

Hisoblang: \(\frac{4 \cdot \frac{2}{2025} \cdot \frac{6}{2026} - 2}{\frac{2023}{2025} \cdot \frac{7}{2026} - \frac{3}{5} \cdot \frac{5}{2026}}\)

Hisoblang. \(\left( \frac{45}{63} - \frac{44}{84} \right) : \left( \frac{21}{3} - 1\frac{1}{9} \right) - \frac{4}{3} : 3\frac{1}{2}\)

Hisoblang: \(1+2−3−4+5+6−7−8+⋯+2021+2022−2023−2024\)

Hisoblang: \(1−2+3−4+5−6+7−8+⋯+2023−2024+2025\)

Hisoblang: \( \frac{1+1}{1+2} \cdot \frac{2+1}{2+2} \cdot \frac{3+1}{3+2} \cdot \dots \cdot \frac{99+1}{99+2} \)

ifodaning qiymatiga qarama-qarshi sonni toping: \((−4) + (−18) \cdot 3 −(−15): (−3) \cdot 5\)

Hisoblang: \( \frac{7}{6} + \frac{13}{12} + \frac{21}{20} + \frac{31}{30} + \frac{43}{42} \)

Son o'qida \(A(−2\frac{2}{5})\) ; \(B(3\frac{1}{5})\) va \(C(4\frac{3}{5})\) nuqtalar belgilangan. AC kesma uzunligini AB kesma uzunligiga nisbatini toping.

Hisoblang: \( (1 + \frac{1}{2}) \cdot (2 + \frac{2}{3}) \cdot (3 + \frac{3}{4}) \cdot \dots \cdot (12 + \frac{12}{13}) \)

a ning 50 dan kichik nechta natural qiymatida \( \frac{a}{2} + \frac{a}{3} + \frac{a}{4} + \frac{a}{5} + \frac{a}{20} \) ifoda butun son bo'ladi.

Hisoblang: \( (\frac{8}{15} + \frac{3}{5}) : \frac{2}{3} - (\frac{6}{8} - \frac{4}{12}) \cdot 1 \frac{1}{41} \)

Hisoblang: \( ((\frac{2}{4} \cdot \frac{1}{9} \cdot \frac{4}{15} - \frac{1}{3}) \cdot (9 - \frac{6}{7} : \frac{3}{14}) + 2 \frac{1}{3}) \cdot 17 \frac{1}{4} \)

Hisoblang: \( (1 - \frac{3}{5} + \frac{8}{15}) - (3 - \frac{7}{6}) + (\frac{9}{10} - 2) \)

Hisoblang. \( (1 + \frac{1}{2}) (1 − \frac{1}{2} + \frac{1}{4} − \frac{1}{8} + \frac{1}{16} − \frac{1}{32} + \frac{1}{64}) \)

\( (\frac{4}{3} \cdot 8 - 1\frac{3}{4}) : 3\frac{1}{2} \) ni hisoblang.

Agar \(A=\frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \dots+\frac{1}{97} + \frac{1}{99}\) , \(B= 1 + \frac{1}{5} + \frac{1}{7} + \dots+\frac{1}{99} + \frac{1}{101}\) , \(C= 1 + \frac{1}{3} + \frac{1}{5} + \dots+\frac{1}{97} + \frac{1}{99}\) va \(D=\frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \dots+\frac{1}{99} + \frac{1}{101}\) bo'lsa, \(A⋅B−C⋅D\) ifodaning qiymatini hisoblang.

Agar \(a=\frac{1}{100}\) , \(b=\frac{1}{86}\) va \(c=\frac{3}{40}\) bo'lsa, \(\frac{c-a}{ac}-\frac{c-b}{bc}\) kasrning qiymatini toping.

Kasrni hisoblang : ( 3 1−3 4 + 3 4−1 3 ) : 1 12

Hisoblang: √ 2117! 2116! + 2115! + √ 17! 15! + 16!

Hisoblang: 1−3+5−7+11−13+⋯+2021−2023+2025−2027 1−2+3−4+5−6+⋯+2021−2022+2023−2024

Hisoblang: 14 2 5 : (7 1 12 + 2.15 −5 19 30)

Ifodani soddalashtiring: $$ \frac{1}{1} + \frac{1}{1+2} + \frac{1}{1+2+3} + \dots + \frac{1}{1+2+3+\dots+n} $$

Hisoblang: $$(8\frac{2}{3} - 3\frac{6}{7}) : \frac{202}{7} + (8\frac{8}{9} \cdot 2\frac{1}{80}) : (1\frac{2}{23} \cdot 1\frac{1}{45})$$

Agar $A=\frac{3}{2} + \frac{33}{22} + \frac{333}{222} + \frac{3333}{2222}$ va $B=\frac{5}{3} + \frac{55}{33} + \frac{555}{333}$ bo'lsa, $A+B$ ni toping.

Hisoblang: $$ \frac{193}{55} : (1\frac{5}{12} + 5\frac{1}{60}) - (-\frac{5}{11} - \frac{1}{44}) : 3\frac{9}{4} $$

Hisoblang: $$ \frac{3}{7} - \frac{2}{5} + \frac{9}{49} - \frac{4}{25} + \frac{27}{343} - \frac{8}{125} + \dots $$

$$\frac{2}{4} + \frac{23}{44} + \frac{223}{444} + \frac{2223}{4444}$$ yig'indining qiymati qaysi oraliqda yotadi?

Agar \(a\) va \(b\) ratsional sonlar uchun \(a + b\sqrt{3} = 3\) tenglik o'rinli bo'lsa, \(a^2 + b^2\) ning qiymatini toping.

Hisoblang: \(\frac{2^3 + 1^6}{8^2 - 5^2} - 2^3 \cdot 1^6\)

Hisoblang: \(2 \cdot (1 - \frac{1}{2}) + 3 \cdot (1 - \frac{1}{3}) + 4 \cdot (1 - \frac{1}{4}) + \dots + 10 \cdot (1 - \frac{1}{10})\)

Agar \(a = (2 - \frac{1}{2}) \cdot (2 - \frac{1}{3}) \cdot (2 - \frac{1}{4}) \cdot \dots \cdot (2 - \frac{1}{10})\) va \(b = (1 + \frac{1}{3}) \cdot (1 + \frac{1}{5}) \cdot (1 + \frac{1}{7}) \cdot \dots \cdot (1 + \frac{1}{19})\) bo'lsa, \(a \cdot b\) ning qiymatini toping.

Hisoblang: \((\frac{2020^5}{6} - \frac{2019^1}{3}) \cdot (\frac{2019^1}{6} - \frac{2018^2}{3})\)

Hisoblang: \(11 - 13 + 15 - 17 + \dots + 2023 - 2025\)

Hisoblang: \(\frac{1}{60} + \frac{1}{120} + \frac{1}{200} + \frac{1}{300} + \frac{1}{420}\)

Hisoblang: \(\frac{1}{2 \cdot 3} + \frac{1}{6 \cdot 5} + \frac{1}{10 \cdot 7} + \frac{1}{14 \cdot 9} + \dots + \frac{1}{138 \cdot 71}\)

Hisoblang: \(\frac{2025^4}{9} \cdot \frac{2023}{19} - \frac{2026^4}{9} \cdot \frac{2022}{19}\)

Hisoblang: \(\frac{1}{2} + \frac{1}{3} - \frac{1}{6} + \frac{4}{6} - \frac{1}{2} + \frac{1}{3} + \frac{3}{2} - \frac{5}{6} - \frac{1}{3} + \frac{4}{6} + \frac{1}{3} - \frac{1}{2}\)

Hisoblang: \(\frac{3}{4} : \frac{5}{6} + \frac{2}{1}\)

Hisoblang: \(\frac{5}{9} - \frac{1}{1} : \frac{1}{1}\)

Agar \(\frac{a}{1+a} + \frac{b}{1+b} + \frac{c}{1+c} = 3\) bo'lsa, \(\frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}\) ning qiymatini toping.

29! + 30! yig'indi qanday eng kichik natural songa bo'linmaydi?

Hisoblang: \(\left( \frac{4!}{4!} + 120 + 0! \right) !\)

Hisoblang: \(\frac{13 \cdot 86}{450} : \frac{26}{100} + 57 \cdot \frac{14}{27} \cdot \frac{2}{5} - \frac{10}{9}\)

Hisoblang: 1 1⋅2⋅3 + 1 2⋅3⋅4 + 1 3⋅4⋅5 + ⋯+ 1 10⋅11⋅12

Hisoblang: 2 3! + 3 4! + 4 5! + ⋯+ 99 100!

Hisoblang: 3 1^2⋅2^2 + 5 2^2⋅3^2 + 7 3^2⋅4^2 + ⋯+ 19 9^2⋅10^2

Hisoblang: 1 4^2 −1 + 1 6^2 −1 + 1 8^2 −1 + ⋯+ 1 100^2 −1

Agar \(x = \frac{1}{7} - \frac{1}{8}\) bo'lsa, 1 49−1 28+ 1 64−1 1−1 7+1 8 ni \(x\) orqali ifodalang.

Agar \(a = (1 + \frac{1}{3}) (1 + \frac{1}{4}) (1 + \frac{1}{5}) \dots (1 + \frac{1}{29})\) va \(b = (1 - \frac{1}{2}) (1 - \frac{1}{3}) (1 - \frac{1}{4}) \dots (1 - \frac{1}{30})\) bo'lsa, \(ab\) ning qiymatini toping.

Hisoblang: \(\frac{(2 \frac{1}{3} \cdot 1 \frac{1}{2} + 3 \cdot 1 \frac{1}{3}) : \frac{5}{2}}{(1 \frac{1}{2} + 3 \frac{1}{2}) \cdot 1 \frac{1}{5}}\)

Hisoblang: \(\frac{(2 \frac{1}{3} \cdot 1 \frac{1}{2} + 3 \cdot 1 \frac{1}{3}) : \frac{5}{2}}{(1 \frac{1}{2} + 3 \frac{1}{2}) \cdot 1 \frac{1}{5}}\)

Taqqoslang: \(A = 2015 + \frac{1}{2016}\); \(B = 2015 + \frac{1}{1 - \frac{1}{2016}}\); \(C = 2015 + \frac{1}{1 - \frac{1}{1 + \frac{1}{2016}}}\)

Hisoblang: 1900 + 42 2009 2010 1938 + 4 2009 2010 − 2010 −2001 2011 2012 1881 −1872 2011 2012

Hisoblang: \[ \frac{2026 \cdot 2025 - 2024}{2024 \cdot 2025 + 2026} \]

Quydagi yig'indini hisoblang: 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + ⋯+ 41 + ⋯+ 41 (41 ta)

A ning qanday eng kichik natural qiymatida \(\left(\frac{1}{4} + \frac{1}{6} + \frac{1}{15}\right) \cdot A\) ifodaning qiymati butun son bo'ladi?

Agar \(a = 1 + 3 + 5 + \dots + 25\) va \(b = 4 + 12 + 20 + \dots + 100\) bo'lsa, \(\frac{b}{a}\) ning qiymatini toping.

Hisoblang: \(\frac{-7 - (-12)}{20 : (-2) + 5}\)

Agar \( \frac{41}{79} + \frac{148}{51} + \frac{49}{61} = n \) bo'lsa, \( \frac{3}{41} + \frac{5}{51} + \frac{12}{61} \) ni \(n\) orqali ifodalang.

Agar \(m\) va \(n\) o'zaro tub sonlar uchun \( \frac{m}{n} = \frac{1}{7 + \frac{1}{7 + \frac{1}{7}}} \) bo'lsa, \(2m + n\) ning qiymatini toping.

Hisoblang: \( \left( 4 : \frac{4}{7} + 3 : \frac{3}{8} \right) : \frac{3}{5} \)

Hisoblang: \( \frac{\frac{1}{2} + \frac{1}{4} + \frac{1}{6}}{\frac{1}{6} + \frac{1}{9} + \frac{1}{12}} \cdot \frac{\frac{1}{2} + \frac{1}{3} + \frac{1}{4}}{\frac{1}{1} + \frac{1}{2} + \frac{1}{3}} \)

Hisoblang: \( \frac{EKUB(12; 36) \cdot EKUK(12; 36)}{12 \cdot 36} \)

Hisoblang: \(1 + 2 + 3 + \dots + 8\)

Hisoblang: \(\left(\frac{1}{7} + \frac{1}{8}\right) \cdot \frac{3}{5}\)

Hisoblang: \(\left(\frac{14}{15} + \frac{5}{2} + \frac{3}{10}\right) \cdot \frac{8}{7} : \frac{3}{4} + \frac{5}{10}\)

Hisoblang: \(\left(\frac{2}{7} + \frac{4}{7} + \frac{6}{7} + \frac{8}{7} + \frac{10}{7} + \frac{12}{7}\right) : \frac{3}{5}\)

Hisoblang: \(\frac{1}{2} \cdot \frac{3}{5} + \frac{2}{3} \cdot \frac{3}{5} - \frac{3}{5} \cdot \frac{3}{5} - \frac{1}{2}\)

Hisoblang: \(\frac{1}{4} + \frac{1}{3} + \frac{1}{9} - \frac{1}{2} + \frac{1}{3}\)

Hisoblang: \(\frac{-7 - (-12)}{(-4)} : \frac{20}{(-2)} + 5\)

Hisoblang: \[ \frac{\frac{2}{15} + \frac{1}{12}}{103 - (2 \div \frac{1}{4}) \cdot \frac{3}{2}} \cdot 30 \]

-1,25 soniga qarama-qarshi bo'lgan sonning teskarisi 0,1 dan qanchaga katta?

0,372 + 3,649 + 4,8463 yig'indining qiymatini yuzdan birlar xonasigacha yaxlitlang.

12,37267 - 8,674 ayirmaning qiymatini mingdan birlar xonasigacha yaxlitlang.

Hisoblang: 3,6 ⋅ 4,8 + 5,4 ⋅3,6 + 4,8 ⋅9,2 −4,8 ⋅5,6.

Rasmda 𝐴 va 𝐵 nuqtalar son o'qida tasvirlangan. 2𝐴+ 𝐵 ning son qiymatini toping.

Hisoblang: \(2,2 + 2,2 + \dots+ 2,2\) (8 ta) + \(1,1 + 1,1 + \dots+ 1,1\) (16 ta)

Hisoblang: \(-\left(-3,8\right) + \left(-6,2\right) - \left(-\left(+2,8\right) + \left(-8,4\right)\right)\)

Hisoblang: \(-16,28 + 8,192 - 2,131 + 9,42\)

Hisoblang: \(83,4 \cdot 0,625 - 3,34 \cdot 2,5 - 8,34 \cdot 3,75\)

Hisoblang: \(9,142 + 2,76 \cdot 0,86 - 9,14 \cdot 6,38\)

Hisoblang: \(12,4: 3,1 + (1,2 \cdot 8,5 - 6,3 \cdot 2,8): 0,3\)

Hisoblang: \(\frac{0,0432}{0,16} + \frac{0,099}{0,3} + \frac{0,128}{0,008}\)

Hisoblang: \(\frac{6,84 \cdot 3,28 + 3,42}{1,14 \cdot 14,24 - 6,68 \cdot 1,14}\)

Hisoblang: \(7,16 \cdot (8,21 - 6,18) + 12,84 \cdot (7,81 - 5,78)\)

Hisoblang: \(\frac{222}{333} + \frac{444}{666} + \frac{666}{999}\)

Hisoblang: \(11,2 \cdot 4,25 \cdot(13,36 -3,36)\)

Hisoblang: \(14,7 \cdot 13 -3 \cdot 14,7\)

Hisoblang: \(\frac{1}{3} \cdot 4 \cdot \frac{1}{5} -4,2 \cdot \frac{2}{3}\)

Hisoblang: \(\frac{1}{3} \cdot \frac{4}{5} + 0,2 \cdot \frac{2}{3}\)

Hisoblang: \((37,3 + 21,7) \cdot 13\)

Hisoblang: \((35,3 + 23,7) \cdot 14\)

Hisoblang: (18,8 −12,8) ⋅18

Soni taqqoslang: 𝑎= (10 −0,2)^2, 𝑏= 10^2 −0,2^2, 𝑐= 10^2 −0,2

Soni taqqoslang: 𝑎= (10 −0,1)^2, 𝑏= 10^2 −0,1^2, 𝑐= 10^2 −0,1

Hisoblang: 7,16 ⋅(8,21 −6,18) +12,84 ⋅(7,81 −5,78)

Hisoblang: (2,5+11/2)⋅2,5+((6−6/5):6+1/5) 0,5⋅(4+ 4/10):4

Hisoblang: (2,3+5:25 4 )⋅20 0,8⋅0,125+30,9

Hisoblang: (29 27−1 9⋅4 3)⋅0,6 (43 18−19 36)⋅1 67+35 36

Hisoblang: (0,125 − 1 18+1 8 1 18 ): ( 2 9 + 7 45 2 15−1 18 ) + 1 2+ 6 13

Hisoblang: 13,5: 2,7 + (1,3 ⋅6,5 −4,6 ⋅3,2): 0,3

Hisoblang: −15,68 + 7,208 −2,124 + 8,86

Hisoblang: −16,31 + 9,189 −1,134 + 8,35

Hisoblang: −16,34 + 8,196 −2,128 + 9,36

Son o'qida 2,4 va 3,5 sonlar orasida maxraji 10 ga teng va surati butun son bo'lgan nechta oddiy kasr joylashgan?

Son o'qida 3,7 va 4,4 sonlar orasida maxraji 10 ga teng va surati butun son bo'lgan nechta oddiy kasr joylashgan?

Hisoblang: 1 + (1 −0,5) (1 − 1 3) (1 −0,25)

3 ga qarama qarshi sonni toping.

Hisoblang: \( (-1,2): (-0,2) + 5 \).

Hisoblang: \(\frac{1}{3} + 0,2\).

Hisoblang: \(\frac{1}{3} + 0,1\).

MS-DTM \( \{-1,6\} [−1,6] − [6,6] \{6,6\} \) ni hisoblang. Bunda [𝑎] - sonning butun qismi, {𝑎} - sonning kasr qismi.

Hisoblang: \( \frac{2}{1} - \left( \frac{1}{2} - \frac{1}{7} \right) \)

Hisoblang: \( \{3[\lg 5] -5 \{\lg \frac{1}{10}\} + 7[\ln 3]\} \)

Soddalashtiring: \( \frac{|a-b| + |b-c| -|a-c|}{|a+b| + |b-c| -|a+c|} \) agar \(a = \lg 3\), \(b = \cos 3\), \(c = \ln 3\)

Agar \( \frac{1}{2} < x < 2 \) bo'lsa, \( ||3x-1| -x| -|x-2| \) ifodani soddalashtiring.

0,1 ⋅0,2 ⋅0,3 −0,2 ⋅0,3 ⋅0,4 + 0,3 ⋅0,4 ⋅0,5 ifodasining qiymatini yuzdan birlar xonasigacha yaxlitlang.

Hisoblang: \( \frac{2}{1} : \frac{1}{97} - \frac{1}{8} \) \( \frac{3}{16} - \frac{1}{4} \)

Agar \(a = 0,2 + 0,02 + 0,002 + \dots\) va \(b = 0,4 + 0,04 + 0,004 + \dots\) bo'lsa, \(7a+b\) ni toping.

Hisoblang: \( \frac{(2,5 - 7,5) \cdot 0,5}{(2 - 1,8) : 0,4} + \frac{(\frac{6}{5} - \frac{3}{14}) \cdot \frac{5}{6}}{(2 - 1,25) : 2,5} \)

Hisoblang : \( \left( \left( \frac{21}{5} - \frac{69,36}{3,4} \right) \cdot 1,5 - \frac{1}{2} \right) \cdot \frac{1}{3} \)

Ifodaning qiymatini toping. $$ \frac{(7.189)^2 + (5.189)^2}{(6.189)^2 + (0.7)^2} $$

Hisoblang: $$ \frac{2(0.1 + 0.01 + 0.001)}{0.222 \times 10^{-3}} $$

Hisoblang. $$ \frac{\frac{11.11}{0.11} + 1 + 0.25}{1 - \frac{1.25}{0.02} : 0.1} $$

$$a = 0.25 \cdot (0.6 + 1.4) + 0.5$$ va $$b = \frac{0.2}{0.001 \cdot (0.05 + 0.19)}$$ bo'lsa, $$b:a$$ ni toping.

Hisoblang: $$ \left(4\frac{1}{8} - 0.004 \cdot 300\right) : 29.25 + \left(4\frac{1}{5} - 3\frac{1}{2}\right) : 70 $$

Hisoblang: $$ \frac{(10 - 1.1: 0.23) \cdot 0.46 + 1.8}{2.75 - 27 \cdot \frac{5}{1}} $$

Hisoblang: \(17 \cdot 54 \cdot 0,8\)

Hisoblang: \(\frac{0,128}{3,2} + \frac{0,86}{5}\)

Hisoblang: \(\frac{6}{5} \cdot 1,2 + \frac{0,8}{\frac{1}{3} \cdot (63 - 13) \cdot 3,6}\)

Hisoblang: \(\frac{0,505 \cdot 2}{5 - 0,002}\)

Hisoblang: \((0,319 \cdot (-\frac{2}{7}) - 1,781 : 3,5) : 0,048\)

Hisoblang: \(\frac{0.429}{0,03} + \frac{0,128}{0,08} + \frac{0,0096}{0,012}\)

Hisoblang: \(12\frac{4}{5} \cdot 3\frac{3}{4} - 4\frac{4}{11} \cdot 4,125\)

Hisoblang: \( (2\frac{1}{3} + 3,5) : (-4\frac{1}{6} + 3,25) + 2\frac{4}{11} \)

Hisoblang: \( \frac{2}{3} \cdot 1.9 + 19.5 : \frac{41}{2} - \frac{62}{75} - 0.16 \)

Hisoblang: \( (2 \frac{1}{3} + 3.5) : (-4 \frac{1}{6} + 3.25) + 2 \frac{4}{11} \)

Hisoblang: \( \frac{3.2 \cdot 5.7 + 3.2 \cdot 4.3}{2.4 \cdot 76 + 2.4 \cdot 24} \)

Hisoblang: \( \frac{1}{5} : ( \frac{17}{40} + 0.6 - 0.005 ) \cdot 1.7 \)

Hisoblang: 3,2 ⋅5,7 + 3,2 ⋅4,3 + 3,2 ⋅1,8 1,6 ⋅6,6 + 1,6 ⋅1,4 + 1,6 ⋅3,8

Hisoblang: 0,4 + 8 ⋅(5 −0,8 ⋅5 8) −5: 2 1 2 (1 7 8 ⋅8 −(8,9 −2,6: 2 3)) ⋅34 2 5 ⋅90

Tenglamani yeching. 14, 32 −4, 92 7, 12 −2, 32 = 1,08: 0,27 𝑥

Hisoblang: 14 ( 0,5 − 1 0,5 − 1 0,5 −1 0,5)

Hisoblang: 19,6 ⋅2 1 2 −(2,625 −1 5 12) : 1 8

Hisoblang: 5, 342 + 10,68 ⋅3,66 + 3, 662 9 ⋅12,72 + 5,28 ⋅(4,73 + 4,27)

4 13 ning kasr qismini 2016 − raqamini toping.

8,6(7) −3, (8) ni hisoblang.

𝑥=3,61(91), 𝑦= 3,62, 𝑧= 3,6(191) va 𝑡= 3,619(1) sonlarini kamaytirish tartibida yozing.

0,6(8) son 0, (31) sondan necha marta katta?

Hisoblang: \(4,(2)+4,(4)+4,(6)\) / \(4,(3)+4,(5)+4,(7)\)

Hisoblang: \(0,4(2)−0,2(8)\) / \(0,(8)+0,(7)\)

Hisoblang: \((1,08 - \frac{2}{25}) : \frac{4}{7} - 0,25 : 0, (33) + 0, (8)\)

Hisoblang: \((0, (2) + 3,6(1)): (\frac{1}{56} -1,91(6)) + 42,5\)

Hisoblang: \(\frac{4,(8)+4,(6)+4,(4)}{4,(5)+4,(3)+4,(1)}\)

Sonni cheksiz davriy o'nli kasr ko'rinishida ifodalab, verguldan keyingi 20-o'rinda turgan raqamini toping: 4/33

Hisoblang: \(6,\overline{8}+6,\overline{7}+6,\overline{5}\) va \(5,\overline{7}+5,\overline{8}+5,\overline{6}\)

Sonlarni o`sish tartibida yozing: \(x= 2,\overline{292}\), \(y= 2,\overline{29}\), \(z= 2,293\), \(t= 2,\overline{292}\)

Hisoblang: \(\frac{6,\overline{2}+6,\overline{4}+6,\overline{6}}{6,\overline{1}+6,\overline{3}+6,\overline{5}}\)

2/11 davriy kasrning 50-o'rinda turgan raqamini toping.

Hisoblang: \(2,\overline{36} + 1,\overline{6}\)

MS-DTM Hisoblang: \(4, (36): 3,1(9) + \frac{1}{30}\)

MS-DTM Hisoblang: \( (4,(6) \cdot 2^{\frac{4}{7}} - 3) \cdot 1,0(5) - 0,4 \)

MS-DTM Hisoblang: \(3,0(45) - 1,(08) + 2,0(45)\)

MS-DTM Hisoblang: \( (4,(6) \cdot 2^{\frac{4}{7}} - 3) \cdot 1,0(5) - 1 \)

MS-DTM \(a= 2, (14); b= 2,1(4); c= 2,11(4)\) sonlarni kamayish tartibida joylashtiring.

MS-DTM Quyidagilardan nechtasi ratsional son bo'ladi: a) \(\frac{22}{7}\), b) \(\frac{7}{17}\), c) \(2 + \lg 3\), d) \(\sqrt{1 + \sqrt[3]{2}}\), e) \(\sqrt{\ln e^4} + \sqrt[3]{\sqrt{8}} - 1\)

Hisoblang: (0,4(6) − 3/2 ⋅ 0,(1)) ⋅ (1/14 + 1/21 + 1/42) ning qiymatini birlar xonasigacha yaxlitlang.

Hisoblang: (0,7(2) + 1/6) : (1,1(6) − 0,5) ⋅ 33/4

𝑎 va 𝑏 o'zaro tub natural sonlar. 𝑎/𝑏 = 3,41(6) bo'lsa, 𝑎 + 𝑏 ning qiymatini toping.

𝑎, 𝑏, 𝑐 raqamlar uchun 𝑎, 𝑏(𝑐) + 𝑏, 𝑐(𝑎) + 𝑐, 𝑎(𝑏) = 24,(4) bo'lsa, 𝑎 + 𝑏 + 𝑐 ning qiymatini toping.

Hisoblang: (3⋅1/8 + 4,8(3) − 0,(3)) / (7,3 − 0,4⋅8,5)

Hisoblang: (1 + 1/0,(9)) ⋅ (1 + 1/1,(9)) ⋅ (1 + 1/2,(9)) ⋅ … ⋅ (1 + 1/9,(9))

Hisoblang. \(0,4\overline{(3)} + 0,6\overline{(2)} \cdot \frac{1}{2} - \frac{1}{2} + \frac{1}{3}\) : \(0,5\overline{(8)} : \frac{50}{53}\)

Agar \(123,\overline{(123)} + 12,\overline{(12)}\) yig'indi berilgan bo'lsa, verguldan keyingi 2025-o'rinda qaysi raqam turadi?

Hisoblang: \(\left(3,\overline{(6)} \cdot 1\frac{5}{6} - 2\right) \cdot 0,\overline{(3)} : 0,6\)

Hisoblang: \(0,8\overline{(3)} - 0,4\overline{(6)}\)

Hisoblang: 20, (25): 1 3 3 10 + 1 6 7

Hisoblang: 6,(8)+6,(7)+6,(5) 5,(7)+5,(8)+5,(6)

Hisoblang: 12⋅0,8−1,8 2,08(3)+2,0(6)−0,25

Hisoblang: (0,75)² −(0,25)² (0,3)² + 0,6 ⋅0,7 + (0,7)²

Hisoblang: (1 −0,5)(1 −0, (3))(1 −0,25) … (1 −0,05) (1 + 0,5)(1 + 0, (3))(1 + 0,25) … (1 + 0,05)

Hisoblang: 7 16 ⋅ 0,(7)+ 1 0,(7)+2 0,(81)+ 1 0,(81)+2

Hisoblang: \(0, (9) + 1, (9) + 2, (9) + ⋯+ 99, (9)\)

Hisoblang: \(\left(3\frac{1}{4} - 2.41\overline{6}\right) : 0.8\overline{3} + 1\frac{1}{2}\)

Hisoblang: \(\frac{7}{176} \cdot 0. (7) + \frac{1}{0. (7)} + 2 \cdot 0. (81) + \frac{1}{0. (81)} + 2\)

Hisoblang: \(\frac{0. (9) + 1. (9) + 2. (9) + ⋯+ 9. (9)}{4 \cdot 0. (09) : 8} \cdot \frac{11}{0.1}\)

Hisoblang: \(\frac{2.4(0. (43) + 0. (23))}{\left(\frac{4}{3} \cdot 2\frac{1}{3} - 4\frac{2}{3} \cdot 1. (6)\right) \cdot 3}\)

Hisoblang: \(\frac{2. (3) + 3. (2)}{2.3 + 3.2}\)

Hisoblang: \(2 \cdot 5^1 + 0.8 \cdot 1.7\)

Hisoblang: \(0.23\overline{7} + \frac{43}{450} - (0.5\overline{61} - \frac{113}{495})\)

Hisoblang: \(0.\overline{9} + 1.\overline{9} + \dots + 99.\overline{9}\)

Hisoblang: \(\frac{0.0\overline{6}}{0.06} + \frac{0.0\overline{8}}{0.08} + \frac{10}{9}\)

Agar \(x < -1\) va \(y > 1\) bo'lsa, quyidagi javoblardan qaysi biri har doim o'rinli?

Agar \(27,3 \cdot 10^n = 0,0000273\) bo'lsa, \(n\) ni toping.

Agar \(47,8 \cdot 10^n = 0,0000478\) bo'lsa, \(n\) ni toping.

Hisoblang: \(0,0016 \cdot 0,004 \cdot 0,050 \cdot 10^6\)

Hisoblang: \((−9)^3 : (−9)^2 + (−10)^3 : (−10) −(−2)^8 : (−2)^7\)

Hisoblang: \(0,84 \cdot 10^9 : 7000000\)

Hisoblang: \(0,04 \cdot 10^{-8} \cdot 2,3 \cdot 10^{12}\)

9 ko'paytmani standart shaklga keltiring: $1 \cdot 10^{-1} \cdot 2 \cdot 10^{-1} \cdot 3 \cdot 10^{-1} \cdot 4 \cdot 10^{-1} \cdot 5 \cdot 10^{-1} \cdot 6 \cdot 10^{-1} \cdot 7 \cdot 10^{-1} \cdot 8 \cdot 10^{-1} \cdot 9 \cdot 10^{-1}$

2 ⋅10−2 ⋅ 2 ⋅100 ⋅ 2 ⋅1000 ⋅… ⋅ 2 ⋅100…0 (10 ta nol) ni standart shaklga keltiring.

Hisoblang: $\frac{49 \cdot 81^2 + 15 \cdot 64^3 \cdot 9^3}{12^9 + 45 \cdot 6^8} \cdot (0, (4))^{-1}$

Hisoblang: $\frac{(27+79) \cdot (2+16/45) \cdot 45^{-1}}{(0,(55)+1/(0,(555)))^2 \cdot 0,(5)}$

Hisoblang: $\frac{(-10)^3}{(-10)^2} + \frac{(-9)^3}{(-9)} - \frac{(-2)^6}{(-2)^5}$

Hisoblang: \(10 \cdot 100 \cdot 1000 \cdot \dots \cdot 10^{\dots} \text{ (10 ta)}\)

Hisoblang: \(2.7 \times 10^{-6} \times 0.03 \times 10^8\)

Hisoblang: \(7 \cdot \underbrace{999...99}_{101 \text{ ta}} + 10\)

Hisoblang: \(0.0032 \times 0.0006 \times 0.050 \times 10^8\)

Hisoblang: \(0.0050 \cdot 0.00016 \cdot 0.008 \cdot 10^8\)

Hisoblang: \(0.0064 \cdot 0.0030 \cdot 0.0005 \cdot 10^6\)

Hisoblang: \(125 \cdot ((5-1)^3 + (5-2)^3 - (5-3)^2) + 5\)

Hisoblang: \(27 \cdot ((3-1)^3 + (3-2)^3 - (3-3)^2) + 3\)

Hisoblang: \(32 \cdot ((2-1)^3 + (2-2)^3 - (2-3)^2) + 2\)

Hisoblang: \(36 \cdot ((6-1)^2 + (6-3)^2 - (6^3)^{-2}) + 6\)

Hisoblang: \(64 \cdot \left( (4-1)^3 + (4-2)^3 - (4-3)^2 \right) + 4\)

Kasrni qisqartiring: \(\frac{10^{n+1} - 4 \cdot 10^n}{10^{n+1} + 5 \cdot 10^n}\)

32 ta \(6^{12}\) yig'indining \(\frac{3}{4}\) qismini toping.

ifodaning \(a = -\frac{1}{6}\) dagi qiymatini toping: \(\( (a-2)^{-3} \cdot (a^3)^{-1} \cdot a^{-2} \right)^3 : a\)

Hisoblang: \(27 \cdot \left( (3-1)^3 + (3-2)^3 - (3-3)^2 \right) + 3\)

Simplify the expression: \(\frac{a^4 \cdot (a^3)^6}{(a^5)^3}\)

Convert the product \(0.009 \cdot 0.02 \cdot 10^6\) to standard form.

If \(x = 2n + 1\) (where \(n\) is a natural number), find the value of the expression \(\frac{(-1)^{x+1} + (-1)^{2x}}{(-1)^x}\).

Simplify the expression (where \(a \neq 0\)): \(\frac{((−2a)^3)^{14}}{((−2a)^4)^{10}}\)

Calculate: \(\frac{2^{23}+2^{23}+2^{23}+2^{23}+2^{23}+2^{23}}{16^6+16^6+16^6}\)

Hisoblang: \(70 \cdot 10^{-5} + 1,8 \cdot 10^{-4}\)

Hisoblang: \(\frac{5^{12} \cdot (2^4)^3}{(2^7)^2 \cdot 128 \cdot (2^{-4})^{-3} \cdot 4^{-5}}\)

Agar \(a = 6^{3x - 2y}\) va \(b = 6^{3x + 2y}\) bo'lsa, \(4 \cdot 6^x + 3 \cdot 6^y\) ni \(a\) va \(b\) orqali ifodalang.

Toping: \(\frac{x^{12} \cdot (x^{-3})^{-5}}{(x^{-4})^{-4} \cdot (x^2)^7}\) ifodaning \(x = 3\) dagi qiymatini

Toping: \((−x^3)^4 \cdot (x^2)^3 : (−x^5)^3\) ifodaning \(x = -2\) dagi qiymatini

Kasrni qisqartiring: 3𝑚+1+31−𝑚 (9𝑚+1)(32−𝑚+31−𝑚)

Agar \(3x = 2\) bo'lsa, \(243x^3 + \frac{5 \cdot 27x}{8} - 81x\) ning qiymatini toping.

Hisoblang: \(\left(\left(\frac{7}{4}\right)^8 - \frac{(2-2)^{-3}}{3^2}\right) \cdot 47^{-1}\)

Hisoblang: \(\frac{4^3}{256} + \frac{3^4}{243} - 2^{-2}\)

Kasrni qisqartiring: \(\frac{(-3n - 3^{-n-1})^2}{9^{n-1}}\)

Soddalashtiring: \[\frac{(3k+7 \cdot 3^k)^3}{(9k+9 \cdot 9^k)^2} = ?\]

Soddalashtiring: \[ \frac{(-3a)^4 \cdot (-3a)^4 \cdot \dots \cdot (-3a)^4 \text{ (12 ta)} }{(-3a)^4 \cdot (-3a)^4 \cdot \dots \cdot (-3a)^4 \text{ (8 ta)}} \]

Agar ifodada \((-2a)^5\) dan 8 ta, \((-2a)^3\) dan 13 ta bo'lsa, ifodani soddalashtiring: \[ \frac{((-2a)^5)^8}{((-2a)^3)^{13}} \]

Kasrni qisqartiring: \[ \frac{2^{n+2}+2^{n+1}+2^n}{2^n-2^{n-3}} \]

Soddalashtiring: (\(\frac{a}{b}\) \(\frac{a}{b}\) \(\dots\) \(\frac{a}{b}\) \(n \text{ marta}\)) \(\cdot\) (\(\frac{b}{a}\) \(\frac{b}{a}\) \(\dots\) \(\frac{b}{a}\) \(n \text{ marta}\)) + 1, bunda \(a, b, n \in \mathbb{N}\)

Soddalashtiring: (\(\frac{a^m}{b^m}\))^n : (\(\frac{a^n}{b^n}\))^m + 1, bunda \(a, b, n, m \in \mathbb{N}\)

Soddalashtiring: \(\frac{(3k+1+7\cdot3^k)^3}{(9^k+1+9^k)^2}\)

Hisoblang: 64 \(\cdot\) (\( (4-1)^3 + (4-2)^3 - (4-3)^2 \)) + 4

Hisoblang: \(\frac{2^5}{2^4} \cdot 2\)

Hisoblang: \[ \frac{25 \cdot 3^4}{2^4 \cdot 3^3} \]

Hisoblang: \[ \frac{5^{12} \cdot (2^4)^3}{(3^3)^2 \cdot 128 \cdot (2^{-4})^{-3} \cdot 4^{-5}} \]

Agar \(a = 6^{3x-2y}\) va \(b = 6^{3x+2y}\) bo'lsa, \(5 \cdot 6^{2x} - 3 \cdot 6^{-2y}\) ni \(a\) va \(b\) orqali ifodalang.

Hisoblang: \[ \frac{(0.5)^{12} \cdot 8^4 - (-4)^3}{1} \]

Kasrni qisqartiring: \(\frac{10^n+1 - 2 \cdot 10^n}{10^n+1 + 2 \cdot 10^n}\)

Hisoblang: \( (1 - (1 - (1 - (1 - (2^{-1}) - 2) - 3) - 1) - 1) \)

Hisoblang. \(810.75 \cdot 32^{-2} - \frac{2}{5} - 270.(3) \cdot 16^{-0.5} + \frac{256}{12}\)

Hisoblang: \(\frac{2^4 + 2^2 + 1}{2^7 - 2^3} + \frac{3^4 + 3^2 + 1}{3^7 - 3^3} + \frac{4^4 + 4^2 + 1}{4^7 - 4^3}\)

Hisoblang: \( (((1 - 2^{-1}) - 1) - 3^{-1}) - 1) - 4^{-1}) - 1) \)

Hisoblang: \( (((1 - 2025^{-1}) - 1) - 1) - 2023) - 1 \)

Hisoblang: $$ \frac{8! + 7! + 6!}{8! - 7! + 6!} $$

J.Saidxonov Mocks Ko'paytmaning qiymatini toping: $$ S = 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2 \cdot 3}} \cdot 3^{\frac{1}{3 \cdot 4}} \cdot 3^{\frac{1}{4 \cdot 5}}} \cdot \dots $$

J.Saidxonov Mocks Ifodaning qiymati quyidagilardan qaysi biriga teng? $$ \left(1 + \frac{1}{3}\right) \left(1 + \frac{1}{3^2}\right) \left(1 + \frac{1}{3^4}\right) \dots \left(1 + \frac{1}{3^{128}}\right) $$

J.Saidxonov Mocks Hisoblang: $$ \left(2 - \frac{1}{2}\right)^{-6} - \left(0.125\right)^{-1} + \left(2\frac{1}{2}\right)^0 $$

J.Saidxonov Mocks $$ n = 2^{13} \cdot 3^6 \cdot 7^4 \cdot 11^3 $$ sonining nechta 3 ga bo'linmaydigan toq bo'luvchisi bor?

Hisoblang: \(1 + \frac{2}{2025} + \frac{3}{2025^2} + \frac{4}{2025^3} + \dots\)

Hisoblang: \(125 \cdot 10^{-3} + \frac{15}{8} + 2\)

Hisoblang: \(\frac{3^3+9^3+15^3+\dots+6075^3}{1^3+3^3+5^3+\dots+2025^3}\)

Hisoblang: \((4-0.25 - 20.5) (4-0.25 + (2\sqrt{2})^{\frac{1}{3}})\)

Hisoblang: \(\frac{(13!)^2+(12!)^2}{(13!)^2-(12!)^2}\)

71456 ⋅ 61567 ko'paytmaning oxirgi ikkita raqamini toping.

Hisoblang: \(10^2+10\)

Hisoblang: \(11^2+11\)

Hisoblang: \(12^2+12\)

Hisoblang: \(13^2+13\)

Hisoblang: \(98^2+98\)

Hisoblang: \(99^2+99\)

−1 −(−1)¹ −(−1)² −⋯−(−1)²⁰²⁴ −(−1)²⁰²⁵ ifodasining qiymati nechaga teng?

Hisoblang: \(\left(81^{\frac{3}{4}} + 64^{-\frac{1}{3}} - 125^{\frac{1}{3}} - \left(\frac{16}{625}\right)^{-\frac{1}{2}}\right)^{\frac{1}{2}}\)

Hisoblang: \(\left(\left(\frac{1}{4}\right)^{-2} - 3 \cdot 8^{\frac{2}{3}} \cdot 40 + \left(\frac{9}{16}\right)^{-\frac{1}{2}} - 3^{-1}\right)\)

Sayxun-Mocks (−(−1)4)3 + (−(−1)3)3 + ((−1)3)3 hisoblang.

Sayxun-Mocks Hisoblang: (\(\frac{1}{2}\))\(^\)−2 + (−2)\(^\)−2 −0,5\(^\)2

Sayxun-Mocks Hisoblang: (−(−1)4)3 + (−(−1)3)3 + ((−1)3)3

Sayxun-Mocks Hisoblang: −(−1)4 + (−(−1)2)3 + (−(−1)5)4

Sayxun-Mocks Hisoblang: \(\frac{2 \cdot 4^9 \cdot 27^3 + 15 \cdot 21^8 \cdot 9^4}{6^9 \cdot 4^5 + 210 \cdot 6^{10}}\)

Sayxun-Mocks Hisoblang: \(\frac{3^4 \cdot 0,328 - 3^3 \cdot 0,628 \cdot 3}{27 \cdot 0,09}\)

Hisoblang: 75 ⋅0,143 −74 ⋅0,843 ⋅7 2401 ⋅0,49

Hisoblang: 2018³ −2017³ −1 2017 ⋅2018

Hisoblang: 2026³ −1998³ −28³ 2026 ⋅1998

𝑎 va 𝑏 natural sonlar uchun \(2^a ⋅ 3^b = 72\) bo'lsa, \(a+b\) ni qiymatini toping.

Hisoblang: \(\frac{10^2+10}{11^2+11} \cdot \frac{12^2+12}{13^2+13} \cdot \dots \cdot \frac{98^2+98}{99^2+99}\)

\(2x = a\) va \(3x = b\) bo'lsa, \(18x\) ni \(a\) va \(b\) orqali ifodalang.

Hisoblang: \(1207 \cdot 24 - 5 \cdot 75 - 2\)

\(3x = \frac{8}{7}\) va \(3y = \frac{189}{8}\) bo'lsa, \(x + y\) ning qiymatini toping.

Agar \(0 < x < 1\) bo'lsa, eng katta sonni toping.

What is the correct answer for question 127?

What is the correct answer for question 128?

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