Question

Simplify : $\frac{6^{\frac{2}{3}}\times \sqrt[3]{6^7}}{\sqrt[3]{6^6}}$

Answer 1

Simplify the given expression:

$\begin{array}{l}\frac{6^{\frac{2}{3}}\times \sqrt[3]{6^7}}{\sqrt[3]{6^6}}\\ =\frac{6^{\frac{2}{3}}\times 6^{\frac{7}{3}}}{6^{\frac{6}{3}}}\left[\because \sqrt[n]{a}=a^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}\right]\\ =6^{\frac{2}{3}+\frac{7}{3}-\frac{6}{3}}\left[\because \frac{a^m\times a^n}{a^p}=a^{m+n-p}\right]\\ =6^{\frac{2+7-6}{3}}\\ =6^{\frac{3}{3}}\\ =6^1\\ =6\end{array}$

The value of the given expression is $\frac{6^{\frac{2}{3}}\times \sqrt[3]{6^7}}{\sqrt[3]{6^6}}=6$