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Find the multiplicative inverse of $$(-7)^{-2}\div (90)^{-1}$$.
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## QuestionMathsClass 8

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

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 $$a^{-b}=\frac{1}{a^b}$$]
$$\implies x=\frac{49}{90}$$.