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Find the multiplicative inverse of \((-7)^{-2}\div (90)^{-1}\).
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Question

Find the multiplicative inverse of \((-7)^{-2}\div (90)^{-1}\).

Answer

Multiplicative inverse of a number is a number which is when multiplied to that number results \(1\).
Let \(x\) be the required multiplicative inverse.
\(\implies \frac{(-7)^{-2}}{90^{-1}}\times x=1\)
\(\implies x=\frac{(90)^{-1}}{(-7)^{-2}}\) [By cross multiplication]
\(\implies x=\frac{(-7)^2}{90}\) [As \(a^{-b}=\frac{1}{a^b}\)]
\(\implies x=\frac{49}{90}\).
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