Math, asked by Sarah06, 1 year ago

simplify and express the result as a rational number

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Answered by Mankuthemonkey01
16
Given question
( \frac{8}{125} ) {}^{ \frac{2}{3} }  \times ( \frac{27}{64} ) {}^{ \frac{ - 2}{3} }  \\  \\  =  >   (( \frac{8}{125} ) {}^{ \frac{1}{3} } ) {}^{2}  \times (( \frac{27}{64} ) {}^{  \frac{  1}{3} } ) {}^{ - 2}  \\  \\  =  >  (\sqrt[3]{ \frac{8}{125} } ) {}^{2}  \times  (\sqrt[3]{ \frac{27}{64} } ) {}^{ - 2}
 =  > ( \frac{2}{5} ) {}^{2}  \times ( \frac{3}{4} ) {}^{ - 2}

 =  >  \frac{4}{25}  \times ( \frac{4}{3} ) {}^{2}

 =  >  \frac{4}{25}  \times  \frac{16}{9}  \\  \\  =  >  \frac{64}{225}

Hope it helps dear friend
Answered by FuturePoet
12

Here your answer goes

Step :- 1 .

Given ,

( \frac{8}{125} )^{}\frac{2}{3}*( \frac{27}{64} )^{}\frac{-2}{3}

( ( \frac{8}{125} ^{\frac{1}{3}} ) )^{2} * ( ( \frac{27}{64} )^{\frac{1}{3} } ) )^{-2}

Step :- 2

( \sqrt[3]{}\frac{8}{125} )^{2} × (\sqrt[3]{}\frac{27}{64} )^{-2}

( 2/5) ^2 * ( 3/4 ) ^-2

Step :- 3

By squaring it will ,

4/25 * ( 4/3) ^2

4/25 × 16/9

==>> \frac{64}{225}

↓↓↓

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