Question

Simplify, giving solution with positive index​ : $4x^2{y}^2÷9x^3{y}^3$

Answer 1

Given , $4x^2{y}^2÷9x^3{y}^3$
It can be written as:
$\frac{4x^2{y}^2}{9x^3{y}^3}$
On further calculation , we have

$\frac{4x^2{y}^2}{9x^3{y}^3}=\frac{4x^{2-3}{y}^{2-3}}{9}$ [$\because$ $\frac{a^m}{a^n}=a^{m-n}$]

$=\frac{4x^{-1}{y}^{-1}}{9}=\frac{4}{9xy}$ [$\because$ $a^{-m}=\frac{1}{a^m}$]

Hence, $\frac{4x^2{y}^2}{9x^3{y}^3}=\frac{4}{9xy}$.