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Bài 8:

a: \(\left(\dfrac{2}{5}+\dfrac{3}{4}\right)^2=\left(\dfrac{8+15}{20}\right)^2=\left(\dfrac{23}{20}\right)^2=\dfrac{529}{400}\)

b: \(\left(\dfrac{5}{4}-\dfrac{1}{6}\right)^2=\left(\dfrac{15}{12}-\dfrac{2}{12}\right)^2=\left(\dfrac{13}{12}\right)^2=\dfrac{169}{144}\)

Bài 1: 

a: \(=5^2\left(5^3-5^2+1\right)=5^2\cdot101⋮101\)

b: \(=7^4\left(7^2+7-1\right)=7^4\cdot55⋮11\)

29 tháng 6 2017

a,\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)

\(=\left(\dfrac{13}{14}\right)^2\)

\(=\dfrac{169}{196}\)

b,\(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)

\(=\left(\dfrac{-1}{12}\right)^2\)

\(=\dfrac{1}{144}\)

c,\(\dfrac{5^4.20^4}{25^5.4^5}\)

\(=\dfrac{100^4}{100^5}\)

\(=\dfrac{1}{100}\)

d,\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4\)

\(=\left(\dfrac{-10}{3}\right)^4.\left(\dfrac{-6}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)

\(=\left(\dfrac{\left(-10\right)}{3}.\dfrac{\left(-6\right)}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)

\(=4^4.\left(\dfrac{-10}{3}\right)\)

\(=256.\left(\dfrac{-10}{3}\right)\)

\(=\dfrac{-2560}{3}\)

28 tháng 9 2021

=0 bạn nha

23 tháng 9 2016

a.\(\left(\frac{3}{7}+\frac{1}{2}\right)^2\)

=\(\left(\frac{6}{14}+\frac{7}{14}\right)^2\)

=\(\left(\frac{13}{14}\right)^2\)

=\(\frac{13^2}{14^2}\)

=\(\frac{169}{196}\)

b.\(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)

=\(\left(\frac{9}{12}-\frac{10}{12}\right)^2\)

=\(\left(\frac{-1}{12}\right)^2\)

=\(\frac{-1^2}{12^2}\)

=\(\frac{1}{144}\).

c.Phần C bn viết lại đề bài đi,mk ko hiểu

d.\(\left(\frac{-10}{3}\right)^5.\left(\frac{-6}{5}\right)^4\)

=\(\frac{-10^5}{3^5}.\left(\frac{-6^4}{5^4}\right)\)

=\(\frac{-100000}{243}.\frac{1296}{625}\)

=\(\frac{-2560}{3}\)

                 Không biết đúng ko nữalolang

23 tháng 9 2016

c.\(\frac{5^4.20^4}{25^5.4^5}\)

=\(\frac{25^2.\left(5.4\right)^4}{25^5.4^5}\)

=\(\frac{1.\left(5\right)^4.\left(4\right)^4}{25^3.4^5}\)

=\(\frac{25^2.1}{25^3.4}\)

=\(\frac{1}{25.4}\)

=\(\frac{1}{100}\).

13 tháng 8 2019

3.

a) \(\left(x-1\right)^3=125\)

=> \(\left(x-1\right)^3=5^3\)

=> \(x-1=5\)

=> \(x=5+1\)

=> \(x=6\)

Vậy \(x=6.\)

b) \(2^{x+2}-2^x=96\)

=> \(2^x.\left(2^2-1\right)=96\)

=> \(2^x.3=96\)

=> \(2^x=96:3\)

=> \(2^x=32\)

=> \(2^x=2^5\)

=> \(x=5\)

Vậy \(x=5.\)

c) \(\left(2x+1\right)^3=343\)

=> \(\left(2x+1\right)^3=7^3\)

=> \(2x+1=7\)

=> \(2x=7-1\)

=> \(2x=6\)

=> \(x=6:2\)

=> \(x=3\)

Vậy \(x=3.\)

Chúc bạn học tốt!

13 tháng 8 2019

Giúp mk với nha các bạn

14 tháng 10 2023

a) \(12\cdot\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\)

\(=12\cdot\dfrac{4}{9}+\dfrac{4}{3}\)

\(=\dfrac{12\cdot4}{9}+\dfrac{4}{3}\)

\(=\dfrac{16}{3}+\dfrac{4}{3}\)

\(=\dfrac{16+4}{3}\)

\(=\dfrac{20}{3}\)

b) \(\left(\dfrac{3}{2}\right)^2-\left[0,5:2-\sqrt{81}\cdot\left(-\dfrac{1}{2}\right)^2\right]\)

\(=\dfrac{9}{4}-\left(\dfrac{1}{2}:2-9\cdot\dfrac{1}{4}\right)\)

\(=\dfrac{9}{4}-\left(\dfrac{1}{4}-9\cdot\dfrac{1}{4}\right)\)

\(=\dfrac{9}{4}-\dfrac{1}{4}\cdot\left(1-9\right)\)

\(=\dfrac{9}{4}+\dfrac{8}{4}\)

\(=\dfrac{17}{4}\) 

c) \(\left(-\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{5}{11}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\)

\(=-\dfrac{1}{12}:\dfrac{5}{11}+\dfrac{1}{12}\)

\(=\dfrac{1}{12}\cdot-\dfrac{11}{5}+\dfrac{1}{12}\)

\(=\dfrac{1}{12}\cdot\left(-\dfrac{11}{5}+1\right)\)

\(=\dfrac{1}{12}\cdot-\dfrac{6}{5}\)

\(=-\dfrac{1}{10}\) 

d) \(\dfrac{\left(-1\right)^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}-\left|-\dfrac{5}{6}\right|\)

\(=-\dfrac{1}{15}+\dfrac{4}{9}:\left(2+\dfrac{2}{3}\right)-\dfrac{5}{6}\)

\(=-\dfrac{1}{15}+\dfrac{4}{9}:\dfrac{8}{3}-\dfrac{5}{6}\)

\(=-\dfrac{9}{10}+\dfrac{1}{6}\)

\(=-\dfrac{11}{15}\) 

e) \(\dfrac{3^7\cdot8^6}{6^6\cdot\left(-2\right)^{12}}\)

\(=\dfrac{3^7\cdot\left(2^3\right)^6}{2^6\cdot3^6\cdot2^{12}}\)

\(=\dfrac{3^7\cdot2^{18}}{2^{6+12}\cdot3^6}\)

\(=\dfrac{2^{18}\cdot3^7}{2^{18}\cdot3^6}\)

\(=3^{7-6}\)

\(=3\)

14 tháng 10 2023

\(a,12\cdot\left(-\dfrac{2}{3}\right)^2+\dfrac{4}{3}\\ =12\cdot\dfrac{4}{9}+\dfrac{4}{3}\\ =\dfrac{16}{3}+\dfrac{4}{3}\\ =\dfrac{20}{3}\\ b,\left(\dfrac{3}{2}\right)^2-\left[0,5:2-\sqrt{81}.\left(-\dfrac{1}{2}\right)^2\right]\\ =\dfrac{9}{4}-\left(\dfrac{1}{2}\cdot\dfrac{1}{2}-9\cdot\dfrac{1}{4}\right)\\ =\dfrac{9}{4}-\left(\dfrac{1}{4}-\dfrac{9}{4}\right)\\ =\dfrac{9}{4}-\left(-\dfrac{8}{4}\right)\\ =\dfrac{17}{4}\)

\(c,\left(-\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{5}{11}+\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\\ =\left(-\dfrac{9}{12}+\dfrac{8}{12}\right)\cdot\dfrac{11}{5}+\left(-\dfrac{3}{12}+\dfrac{4}{12}\right)\\ =-\dfrac{1}{12}\cdot\dfrac{11}{5}+\dfrac{1}{12}\\ =-\dfrac{11}{60}+\dfrac{1}{12}\\ =-\dfrac{1}{10}\)

\(d,\dfrac{-1^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}-\left(-\dfrac{5}{6}\right)\\ =-\dfrac{1}{15}+\dfrac{4}{9}\cdot\dfrac{3}{8}+\dfrac{5}{6}\\ =-\dfrac{1}{15}+\dfrac{1}{6}+\dfrac{5}{6}\\ =\dfrac{1}{10}+\dfrac{5}{6}\\ =\dfrac{14}{15}\)

`e,` Không hiểu đề á c: )

25 tháng 10 2021

\(\left(\dfrac{2}{3}\right)^5-\left(\dfrac{3}{4}\right)^2\cdot\left(-1\right)^5=\dfrac{32}{243}-\dfrac{9}{16}\left(-1\right)=\dfrac{32}{243}+\dfrac{9}{16}=\dfrac{2699}{3888}\)

20 tháng 9 2023

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