Question

Simplify
(i) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}$ .
(ii) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$

Answer 1

(i) $\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}={11}^{\frac{1}{2}-\frac{1}{4}}[\because \frac{a^m}{a^n}=a^{m-n}]$ .
$={11}^{\frac{2-1}{4}}$
$={11}^{\frac{1}{4}}$
(ii) $7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$
$=(7\times 8{)}^{\frac{1}{2}}[\because a^m.b^m=\left(ab{)}^m\right]={56}^{\frac{1}{2}}$