Simplify: $[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}$.

To do: To simplify: $[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}$.

Solution:
 

$[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}$

$=[ ( \frac{1}{(\frac{3}{2})^{2}})-( \frac{1}{3})^{2}]\times( \frac{1}{(\frac{5}{3})^{2}})$        [$\because x^{-n}=\frac{1}{x^{n}}$]

$=[ ( \frac{2}{3})^{2}-( \frac{1}{3})^{2}]\times( \frac{3}{5})^{2}$      [$\frac{1}{( \frac{a}{b})^y}=( \frac{b}{a})^n$]

$=[ ( \frac{2}{3}\times\frac{2}{3})-( \frac{1}{3}\times\frac{1}{3})]\times( \frac{3}{5}\times\frac{3}{5})$

$=[\frac{4}{9}-\frac{1}{9}]\times\frac{9}{25}$

$=[\frac{4-1}{9}]\times\frac{9}{25}$

$=[\frac{3}{9}]\times\frac{9}{25}$

$=\frac{3}{25}$

Thus, $[ ( \frac{3}{2})^{-2}-( \frac{1}{3})^{2}]\times( \frac{5}{3})^{-2}=\frac{3}{25}$.

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Updated on: 10-Oct-2022

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