How do you simplify ${(\frac{2}{5})}^{- 3}$ $(2/5)^-3$ ?

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Answer 1 · 2018-03-24T02:36:24

$\frac{125}{8}$ $125/8$

$\frac{125}{8}$ $125/8$
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Answer 2 · 2018-03-24T02:40:25

$\frac{125}{8}$ $125/8$

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

$\frac{\frac{1}{2^{3}}}{{(\frac{1}{5})}^{3}} = (\frac{1}{2^{3}}) \cdot (\frac{5^{3}}{1})$ $(1/2^3) / (1/5)^3 = (1/2^3) * (5^3/1)$

$\Rightarrow \frac{5^{3}}{2^{3}} = \frac{5 \cdot 5 \cdot 5}{2 \cdot 2 \cdot 2} = \frac{125}{8}$ $=> 5^3 / 2^3 = (5*5*5) / (2 *2 *2) = 125/ 8$

Answer 3 · 2018-03-24T02:45:04

$\frac{125}{8}$ $125/8$

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

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

So , ${(\frac{2}{5})}^{- 3}$ $(2/5)^-3$

$\Rightarrow {(\frac{5}{2})}^{3}$ $=> (5/2)^3$

$\Rightarrow \frac{5^{3}}{2^{3}}$ $=> 5^3/2^3$

$\Rightarrow \frac{5 \times 5 \times 5}{2 \times 2 \times 2}$ $=> (5xx5xx5)/(2xx2xx2$

$\Rightarrow \frac{125}{8}$ $=> 125/8$

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