Question

simplify and express the result as a rational number

Answer 1

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

Answer 2

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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