Question

Simplify :

$\frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}$.

Answer 1

Given; $\frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}$.

$$\begin{gathered} \frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}=\frac{12\times 12\times 12\times 12\times 9\times 9\times 9\times 4}{6\times 6\times 6\times 8\times 8\times 27} \\ =\frac{{\cancel{12}}^{\cancel{2}}\times {\cancel{12}}^{\cancel{2}}\times {\cancel{12}}^{\cancel{2}}\times {\cancel{12}}^{{\cancel{6}}^2}\times \cancel{9}\times 9\times 9\times \cancel{4}}{\cancel{6}\times \cancel{6}\times \cancel{6}\times \cancel{8}\times {\cancel{8}}^{\cancel{2}}\times \cancel{{27}^{\cancel{3}}}} \\ =\frac{2\times 9\times 9}{1} \\ =162 \end{gathered}$$

Hence, $\frac{{12}^4\times 9^3\times 4}{6^3\times 8^2\times 27}=162$.