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Q.

What is the value of ${(\frac{- 2}{3})}^{4}$ ?

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a

(\frac{16}{81})

b

(- \frac{81}{16})

c

(\frac{- 16}{81})

d

(- \frac{81}{- 16})

answer is A.

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Detailed Solution

Given,

{(\frac{- 2}{3})}^{4}

.
We know that

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

where a, b and m are real numbers.

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

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

\Rightarrow {(\frac{- 2}{3})}^{4} = \frac{16}{81}

Hence, option 1 is correct.

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