Evaluate:$[(\frac{-3}{2})^2]^{-3}$

Given :

The given expression is $[(\frac{-3}{2})^2]^{-3}$.

To find :

We have to find the value of the given expression.

Solution :

We know that,

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

$[(\frac{-3}{2})^2]^{-3} =(\frac{-3^2}{2^2})^{-3} $

$= (\frac{9}{4})^{-3}$

We know that,

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

$= (\frac{4}{9})^{3}$

$= \frac{4^3}{9^3}$

$= \frac{64}{729}$

The value of $[(\frac{-3}{2})^2]^{-3}$ is $ \frac{64}{729}$.

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Updated on: 10-Oct-2022

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