Question

Simplify:

$\frac{2\times 3^4\times 2^5}{9\times 4^2}$

Answer 1

$\frac{2\times 3^4\times 2^5}{9\times 4^2}=\frac{2\times 3^4\times 2^5}{3\times 3\times {\left(2\times 2\right)}^2}$

$$\begin{gathered} =\frac{2\times {\left(3\right)}^4\times 2^5}{{\left(3\right)}^2\times {\left(2^2\right)}^2} \\ =\frac{2\times 3^4\times 2^5}{\left(3^2\right)\times 2^{2\times 2}}({\left(a\times b\right)}^x=a^x\times b^x;{\left(a^x\right)}^y=a^{x\times y}) \\ =\frac{2\times 3^4\times 2^5}{3^2\times 2^4} \\ =2^{1+5-4}\times 3^{4-2}(a^x\times a^y=a^{x+y};\frac{a^x}{a^y}=a^{x-y}) \\ =2^2\times 3^2 \\ =4\times 9 \\ =36 \end{gathered}$$

Hence, the simplified form of $\frac{2\times 3^4\times 2^5}{9\times 4^2}$ is $36.$