Question 5: \((iii)\) \(\quad\) \(\sqrt{\frac{( 216)^{\frac{2}{3}} \times ( 25)^{\frac{1}{2}}}{( 0.04)^{-\frac{3}{2}}}}\)
Solution:
\[\begin{align*}
&=\sqrt{\frac{( 216)^{\frac{2}{3}} \times ( 25)^{\frac{1}{2}}}{( 0.04)^{-\frac{3}{2}}}}\\
&=\sqrt{\frac{\left( 6^{3}\right)^{\frac{2}{3}} \times \left( 5^{2}\right)^{\frac{1}{2}}}{\left(\frac{4}{100}\right)^{-\frac{3}{2}}}}\\
&=\sqrt{\frac{6^{2} \times 5}{\left(\frac{1}{25}\right)^{-\frac{3}{2}}}}\\
&=\sqrt{\frac{6^{2} \times 5}{( 25)^{\frac{3}{2}}}}\\
&=\sqrt{\frac{6^{2} \times 5}{\left( 5^{2}\right)^{\frac{3}{2}}}}\\
&=\sqrt{\frac{6^{2} \times 5}{5^{3}}}\\
&=\sqrt{\frac{6^{2}}{5^{2}}}\\
&=\frac{6}{5}\\
\end{align*}\]