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$\displaystyle Find\ the\ value\ of\ \left[( -2)^{-2}\right]^{-4}$.
Given :
$\left[( -2)^{-2}\right]^{-4}$
To find :
We have to find the value $\left[( -2)^{-2}\right]^{-4}$.
Solution :
We know that,
$\left( a^{m}\right)^{n} =( a)^{m\times n}$
Therefore,
$\left[( -2)^{-2}\right]^{-4} =( -2)^{( -2\times -4)}$
$=( -2)^{8}$
$=( -1)^{8} \times ( 2)^{8}$ ($(-1)$ to the power of an even number is equal to 1.)
$=1\times 256$
=256.
The value of $\displaystyle \ \left[( -2)^{-2}\right]^{-4} \ =\ 256$
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