Question

Find:
(i) ${64}^{\frac{1}{2}}$ .

(ii) ${32}^{\frac{1}{5}}$ .

Answer 1

(i) ${64}^{\frac{1}{2}}$

$={\left(2^6\right)}^{\frac{1}{2}}[\because 64=2^6]$

$=2^{6\times \frac{1}{2}}=2^3=8[\because (a^m{)}^n=a^{mn}]$
(ii) ${32}^{\frac{1}{5}}$
$={\left(2^5\right)}^{\frac{1}{5}}[\because 32=2^5]$
$=(2{)}^{5\times \frac{1}{5}}=2[\because (a^m{)}^n=a^{mn}]$