Question

Simplify 64/125 raised to the power 2/3

Answer 1

Answer:

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Answer 2

$given( \frac{64}{125 }) {}^{ \frac{ - 2}{3} }$

$= ( \frac{4 {}^{3} }{5 {}^{3} } ) {}^{\frac{ - 2}{3} }$

$= ( \frac{4}{3 }{ {}^{ \: 3} } ) {}^{\frac{ - 2}{3} }$

$\frac{a {}^{n} }{b {}^{n} } = ( \frac{a}{b} ) {}^{n}$

$= ( \frac{4}{3} ) {}^{3 \times } {}^{ \frac{ - 2}{3} }$

$(a {}^{m} ) {}^{n } = amn$

$= ( \frac{5}{4} ) {}^{2}$

$( \frac{a}{b} ) {}^{ - n} = ( \frac{b}{a} ) {}^{n}$

$= \frac{5 {}^{2} }{4 {}^{2} }$

$= \frac{25}{16}$