Simplify [ (625)^ 1 2 ^ -1 4 ]^2 - Vidyadip

Question

Simplify $\Big[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\Big]^2$

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Answer

We have to simplify$\bigg[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\bigg]^2$. So,$\Bigg[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\bigg]^2=\Bigg[\Big\{\frac{1}{625^{\frac{1}{2}}}\Big\}^{\frac{-1}{4}}\Bigg]^2$
$=\Bigg[\Big\{\frac{1}{5^{4\times\frac{1}{2}}}\Big\}^{\frac{-1}{4}}\Bigg]^2$
$=\Bigg[\Big\{\frac{1}{5^2}\Big\}^{\frac{-1}{4}}\Bigg]^2$
$=\bigg[\Big\{\frac{1}{5^{2\times\frac{-1}{4}}}\Big\}\bigg]^2$
$\Bigg[\Big\{(625)^{\frac{-1}{2}}\Big\}^{\frac{-1}{4}}\Bigg]^2=\Bigg[\bigg\{\frac{1}{5^{\frac{-1}{2}}}\bigg\}\Bigg]^2$
$\bigg[\begin{Bmatrix}\frac{1}{\frac{1}{5^{\frac{1}{2}}}} \end{Bmatrix}\bigg]^2$
$=\bigg[\Big\{1\times5^{\frac{1}{2}}\Big\}\bigg]^2$
$=5^{\frac{1}{2}\times2}=5$
Hence, the value of $\Bigg[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\Bigg]^2$ is 5.

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