Question 7: Simplify the following:
\((ii)\) \(\quad\) \(\large{\sqrt[3]{( 27)^{2x}}} \)
Solution:
\[
\begin{align*}
&=\sqrt[3]{( 27)^{2x}}\\
&=( 27)^{\large{\frac{2x}{3}}}\\
&=\left( 3^{3}\right)^{\large{\frac{2x}{3}}}\\
&=3^{3\times \large{\frac{2x}{3}}}\\
&=3^{2x}
\end{align*}
\]