Question

Simplify and express the answer in the positive exponent form:​
(iii) $\frac{36\times (-6{)}^2\times 3^6}{{12}^3\times 3^5}$

Answer 1

Given, $\frac{36\times (-6{)}^2\times 3^6}{{12}^3\times 3^5}$
It can be written as:
$\frac{36\times (-6{)}^2\times 3^6}{{12}^3\times 3^5}=\frac{6\times 6\times (-6{)}^2\times 3^6}{3^3\times 4^3\times 3^5}$
On further calculation , we have :

$\frac{36\times (-6{)}^2\times 3^6}{{12}^3\times 3^5}=\frac{6^2(-6{)}^2\times 3^{6-3-5}}{4^3}$

$=\frac{6^2(-6{)}^2\times 3^{-2}}{4^3}$
$=\frac{6^2(-6{)}^2}{3^2\times 4^3}$
$=\frac{6\times 6\times -6\times -6}{3\times 3\times 4\times 4\times 4}$

$=\frac{9}{4}=(\frac{3}{2}{)}^2$

Hence, $\frac{36\times (-6{)}^2\times 3^6}{{12}^3\times 3^5}=(\frac{3}{2}{)}^2$