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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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