Express the following in positive exponents only :
${(- 3)}^{2} \times {(5^{2})}^{- 2}$

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Solution

Given that , ${(- 3)}^{2} \times {(5^{2})}^{- 2}$
$= {(- 3)}^{2} \times 5^{2 \times - 2}$ [ Using exponent laws : $a^{- n} = \frac{1}{a^{n}}$ ]
$= {(- 3)}^{2} \times 5^{- 4}$
$= \frac{{(- 3)}^{2}}{5^{4}}$
Hence , the required expression is $\frac{{(- 3)}^{2}}{5^{4}}$ .

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