Write the following using positive exponents only :
${(- 3^{2})}^{- 2} \times (5^{3} \div 5^{4})$

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Solution

Given that, ${(- 3^{2})}^{- 2} \times (5^{3} \div 5^{4})$
$= \frac{1}{{(- 3^{2})}^{2}} \times 5^{3} \times 5^{- 4}$
$= \frac{1}{{(- 1)}^{2} \times 3^{2 \times 2}} \times 5^{3 - 4}$
$= \frac{1}{1 \times 3^{4}} \times 5^{- 1}$
$= \frac{1}{3^{4} \times 5}$
Hence , the required value is $\frac{1}{3^{4} \times 5}$

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