Question

Find the multiplicative inverse of ${10}^{-7}$.

• A. ${10}^{-2}$
• B. ${10}^2$
• C. ${10}^7$
• D. ${10}^6$

Answer 1

The correct option is C

${10}^7$

Multiplicative inverse of a non-zero $x$ is $\frac{1}{x}$; so that when these two are multiplied, the product value is 1. Therefore, the multiplicative inverse of ${10}^{-7}$should be a number which when multiplied with ${10}^{-7}$ gives 1.
Let the multiplicative inverse of ${10}^{-7}$ be $x.$
Then, ${10}^{-7}\times x=1.$
$\Rightarrow x=\frac{1}{{10}^{-7}}={10}^7$
$(\because a^{-n}=\frac{1}{a^n}⟹\frac{1}{a^{-n}}=\frac{1}{\frac{1}{a^n}}=a^n)$
Thus, the multiplicative inverse of ${10}^{-7}$ is ${10}^7.$