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

Question

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

✓

Answer

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

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