Simplify: [ (-1 4 )^2 ^ -2 ]^ -1 - Vidyadip

Question

Simplify: $\Bigg[\bigg\{\Big(\frac{-1}{4}\Big)^2\bigg\}^{-2}\Bigg]^{-1}$

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Answer

$\Bigg[\bigg\{\Big(\frac{-1}{4}\Big)^2\bigg\}^{-2}\Bigg]^{-1}=\Bigg[\Big(\frac{-1}{4}\Big)^{2\times(-2)}\Bigg]^{-1}$ $=\bigg[\Big(\frac{-1}{4}\Big)^{-4}\bigg]^{-1}$ $=\Big(\frac{-1}{4}\Big)^{-4\times(-1)}=\Big(\frac{-1}{4}\Big)^{4}$ $=\frac{-1}{4}\times\frac{-1}{4}\times\frac{-1}{4}\times\frac{-1}{4}$ $=\frac{1}{256}$

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