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The value of ${(\frac{2}{5})}^{- 3}$ is

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\frac{- 8}{125}

\frac{25}{4}

\frac{125}{8}

\frac{- 2}{5}

answer is C.

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Detailed Solution

Given that,

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

is a fraction with exponent.
We have to find the value of

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

.
We are aware of this, based on the exponents' law.

{(\frac{a}{b})}^{- m} = {(\frac{b}{a})}^{m}

We can write given equation as

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

Also we know that

2^{3}

8

and

5^{3}

125

By substituting in above we get

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

\Rightarrow {(\frac{2}{5})}^{- 3} = \frac{125}{8}

Thus, the value of

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

\frac{125}{8}

.
Hence, option 3 is correct.

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