Question 5: \((i)\) \(\quad\) \(\large{\frac{( 25)^{\frac{3}{2}} \times ( 243)^{\frac{3}{5}}}{( 16)^{\frac{5}{4}} \times ( 8)^{\frac{4}{3}}}}\)
Solution:
\[\begin{align*}
&=\frac{( 25)^{\frac{3}{2}} \times ( 243)^{\frac{3}{5}}}{( 16)^{\frac{5}{4}} \times ( 8)^{\frac{4}{3}}}\\
&=\frac{\left( 5^{2}\right)^{\frac{3}{2}} \times \left( 3^{5}\right)^{\frac{3}{5}}}{\left( 2^{4}\right)^{\frac{5}{4}} \times \left( 2^{3}\right)^{\frac{4}{3}}}\\
&=\frac{5^{3} \times 3^{3}}{2^{5} \times 2^{4}}\\
&=\frac{125\times 27}{32\times 16}\\
&=\frac{3375}{512}\\
\end{align*}\]