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Q.

The value of ${(- \frac{5}{8})}^{3}$ is equal to

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a

- \frac{125}{512}

b

- \frac{512}{125}

c

\frac{125}{512}

d

1

answer is A.

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Detailed Solution

Given

{(- \frac{5}{8})}^{3}

.
Apply law of exponent

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

and simplify.

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

= \frac{(- 5) (- 5) (- 5)}{(8) (8) (8)}

= \frac{- 125}{512}

Using the fact that

a^{3} = a \times a \times a

and simplify the expression.
Hence, the correct option is 1.

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