Write the multiplicative inverse of $\frac{5^{-2}}{5^{-4}}$.

Given,

$\frac{5^{-2}}{5^{-4}}$

The multiplicative inverse is nothing but the number which makes the existing number and makes it equal to unity.

Multiplicative inverse of a is $frac{1}{a}.$

$atimes frac{1}{a} =1$

$5^{-2} \div 5^{-4} =\frac{5^{-2}}{5^{-4}} =5^{-2-( -4)} =5^{-2+4} =5^{2} =25$

Multiplicative inverse of $5^{-2} \div 5^{-4} =25$

$\frac{1}{5^{-2} \div 5^{-4}} =\frac{1}{25}$$.$

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Updated on: 10-Oct-2022

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