Question
Simplify:$\Big(16^{-\frac{1}{5}}\Big)^{\frac{5}{2}}$
✓
Answer
We have,$\Big(16^{-\frac{1}{5}}\Big)^{\frac{5}{2}}=16^{-\frac{1}{5}\times\frac{5}{2}}$
$=16^{-\frac{1}{2}}$
$=\frac{1}{16^{\frac{1}{2}}}$
$=\frac{1}{(4^{2})^{\frac{1}{2}}}$
$=\frac{1}{(4^2)^{\frac{1}{2}}}$
$=\frac{1}{4}$
$\Rightarrow\Big(16^{-\frac{1}{5}}\Big)^{\frac{5}{2}}=\frac{1}{4}$
$=16^{-\frac{1}{2}}$
$=\frac{1}{16^{\frac{1}{2}}}$
$=\frac{1}{(4^{2})^{\frac{1}{2}}}$
$=\frac{1}{(4^2)^{\frac{1}{2}}}$
$=\frac{1}{4}$
$\Rightarrow\Big(16^{-\frac{1}{5}}\Big)^{\frac{5}{2}}=\frac{1}{4}$
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