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10 tháng 8 2016

c) Ta co : A=1/2^1+1/2^2+...+1/2^49+1/2^50

2A=1+1/2+1/2^2+........+1/2^48+1/2^49

A=1-1/2^50<1

Vậy A=1/2^1+1/2^2+...+1/2^49+1/2^50 <1

4 tháng 7 2019

\(=\left(2.\left(2^3\right)^4.\left(3^3\right)^2+2^2.\left(2.3\right)^9\right):\left(2^{12}.\left(3^2\right)^3.31\right)\)

\(=\left(2^{13}.3^6+2^{11}.3^9\right):\left(2^{12}.3^6.31\right)\)

\(=\left[2^{11}.3^6\left(2^2+3^3\right)\right]:\left(2^{12}.3^6.31\right)\)

\(=\frac{2^{11}.3^6.31}{2^{12}.3^6.31}=\frac{1}{2}\)

4 tháng 7 2019

Đưa về phân số:

\(=\frac{2.8^4.27^2+4.6^9}{2^{12}.9^3.31}\)

\(=\frac{2.\left(2^3\right)^4.\left(3^3\right)^2+2^2.\left(2.3\right)^9}{2^{12}.\left(3^2\right)^3.31}\)

\(=\frac{2.2^{3.4}.3^{3.2}+2^2.2^9.3^9}{2^{12}.3^{2.3}.31}\)

\(=\frac{2.2^{12}.3^6+2^{2+9}.3^9}{2^{12}.3^6.31}\)

\(=\frac{2^{1+12}.3^6+2^{11}.3^9}{2^{12}.3^6.31}\)

\(=\frac{2^{13}.3^6+2^{11}.3^9}{2^{12}.3^6.31}\)

\(=\frac{2^{11}.3^6\left(2^2+3^3\right)}{2^{12}.3^6.31}\)

\(=\frac{2^{11}.3^6.31}{2^{12}.3^6.31}=\frac{1}{2}\)

Em hiểu hơn ko?

23 tháng 3 2021

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a) \(\dfrac{11\cdot8-11\cdot3}{17-6}\)

\(=\dfrac{11\cdot\left(8-3\right)}{11}=5\)

b) \(\dfrac{24-12\cdot13}{12+4\cdot9}\)

\(=\dfrac{12\cdot\left(2-13\right)}{12\left(1+3\right)}=\dfrac{-11}{4}\)

AH
Akai Haruma
Giáo viên
5 tháng 2

Lời giải:
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.234.8^2}=\frac{(3^2)^4.(3^3)^5.3^6.3^4}{3^8.(3^4)^4.2.3^2.13.(2^3)^2}\)

\(=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.2.3^2.13.2^6}=\frac{3^{33}}{3^{26}.2^7.13}=\frac{3^7}{2^7.13}\)

16 tháng 3 2022

\(e.\dfrac{7}{10}\cdot\dfrac{-3}{5}+\dfrac{7}{10}\cdot\dfrac{-2}{5}-\dfrac{3}{10}\)

\(=\dfrac{7}{10}\cdot\left[\left(\dfrac{-3}{5}\right)+\left(\dfrac{-2}{5}\right)\right]-\dfrac{3}{10}\)

\(=\dfrac{7}{10}\cdot1-\dfrac{3}{10}=\dfrac{4}{10}=\dfrac{2}{5}\)

\(f.\dfrac{-3}{7}\cdot\dfrac{5}{9}+\dfrac{4}{9}\cdot\dfrac{-3}{7}+2\dfrac{3}{7}\)

\(=\dfrac{-3}{7}\cdot\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{17}{3}\)

\(=\dfrac{-3}{7}\cdot1+\dfrac{17}{3}=\dfrac{-9}{21}+\dfrac{119}{21}=\dfrac{110}{21}\)

\(g.\dfrac{5}{9}\cdot\dfrac{10}{17}+\dfrac{5}{9}\cdot\dfrac{9}{17}-\dfrac{5}{9}\cdot\dfrac{2}{17}\)

\(=\dfrac{5}{9}\cdot\left(\dfrac{10}{17}+\dfrac{9}{17}-\dfrac{2}{17}\right)\)

\(=\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)

28 tháng 3 2017

\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.3^5.\left(2^3\right)^2}=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.2^6}=\frac{3^{29}.3^4}{3^{29}.2^6}=\frac{1.81}{1.64}=\frac{81}{64}\)

10 tháng 4 2018

\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.243.8^2}\)

\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.\left(3^5\right).\left(2^3\right)}\)

\(M=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.8}\)

\(M=\frac{3^{33}}{3^{29}.8}\)

\(M=\frac{3^4}{1.8}\)

\(M=\frac{81}{8}\)

Chúc bạn học tốt !!! 

10 tháng 4 2018

Sửa hộ mk : 

\(8^2=2^9\)

Kết quả : \(\frac{81}{512}\)

27 tháng 1 2022

Bài 1:

\(a,=\frac{2}{3}-\frac{16}{3}=\frac{-14}{3}\)

\(b,=\left(\frac{3}{7}+\frac{4}{7}\right)+\left(-\frac{6}{19}+\frac{-13}{19}\right)=1-1=0\)

\(c,=\frac{3}{5}.\left(\frac{8}{9}-\frac{7}{9}+\frac{26}{9}\right)=\frac{3}{5}.3=\frac{9}{5}\)

8 tháng 2 2022

a,\(\dfrac{1}{2}\).\(\dfrac{4}{3}\)-\(\dfrac{20}{3}\).\(\dfrac{4}{5}\)=\(\dfrac{2}{3}\)-\(\dfrac{16}{3}\)=-\(\dfrac{14}{3}\)