Question

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

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)6^{\frac{2}{5}}\times 6^{\frac{3}{5}}=6^{\frac{2}{5}+\frac{3}{5}}=6^{\frac{5}{5}}=6(a^m\times a^n=a^{m+n}) \\ \left(\mathrm{ii}\right)3^{\frac{1}{2}}\times 3^{\frac{1}{3}}=3^{\frac{1}{2}+\frac{1}{3}}=3^{\frac{3+2}{6}}=3^{\frac{5}{6}} \\ \left(\mathrm{iii}\right)7^{\frac{5}{6}}\times 7^{\frac{2}{3}}=7^{\frac{5}{6}+\frac{2}{3}}=7^{\frac{5+4}{6}}=7^{\frac{9}{6}}=7^{\frac{3}{2}} \end{gathered}$$