Question

Simplify:

ii. $\sqrt[5]{5(32{)}^{-3}}$

Answer 1

To simplify : $\sqrt[5]{5(32{)}^{-3}}$

$=(32{)}^{\frac{-3}{5}}$ $\{\because \sqrt[n]{n{a}^m}=a^{\frac{m}{n}}\}$

$=(2^5{)}^{\frac{-3}{5}}$

$=2^{5\times \frac{-3}{5}}$ $\{\because (a^m{)}^n=a^{mn}\}$

$=\left(2^{-3}\right)$

$=\frac{1}{2^3}$ $\{\because a^{-m}=\frac{1}{a^m}\}$

$=\frac{1}{8}$

Therefore, $\sqrt[5]{5{32}^{-3}}=\frac{1}{8}$