Question

Evaluate :
$\frac{3^4\times {12}^3\times 36}{2^5\times 6^3}$

Answer 1

Given $\begin{array}{c}\frac{3^4\times {12}^3\times 36}{2^5\times 6^3}\end{array}$
$\begin{array}{c}=\frac{3^4\times {\left(2^2\times 3\right)}^3\times \left(2^2\times 3^2\right)}{2^5\times {\left(2\times 3\right)}^3}\end{array}$
$\begin{array}{c}=\frac{3^4\times 2^6\times 3^3\times 2^2\times 3^2}{2^5\times 2^3\times 3^3}\end{array}$
$[since,(a\times b{)}^m=a^m\times b^m]$
$\begin{array}{c}=3^{4+3+2-3}\times 2^{6+2-5-3}\end{array}$ [since, $a^m\times a^n=a^{m+n}$]
$=3^6\times 2^0$
$=3^6$
$=729$
Hence, the value of the given expression is $729$