Question
Simplify: $(625)^{-\frac{1}{2}^{-\frac{1}{4}^{2}}}$
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Answer
$\Bigg[\Big((625)^{-\frac{1}{2}}\Big)^{-\frac{1}{4}}\Bigg]^{2}=(25^{-1})^{-\frac{1}{4}\times2}=[(5^2)^{-1}]^{-\frac{1}{4}\times2}$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$ $=5^{-2\times-\frac{1}{4}\times2}=5^1=5$
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