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

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Solution

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

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

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

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

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