Question

Simplify:
(i) $3^{1/4}\times 5^{1/4}$
(ii) $2^{5/8}\times 3^{5/8}$
(iii) $6^{1/2}\times 7^{1/2}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)3^{\frac{1}{4}}\times 5^{\frac{1}{4}}={15}^{\frac{1}{4}}\left[(a^m\times b^m)={\left(ab\right)}^m\right] \\ \left(\mathrm{ii}\right)2^{\frac{5}{8}}\times 3^{\frac{5}{8}}=6^{\frac{5}{8}} \\ \left(\mathrm{iii}\right)6^{\frac{1}{2}}\times 7^{\frac{1}{2}}={42}^{\frac{1}{2}} \end{gathered}$$