Question

The multiplicative inverse of ${10}^{100}$ is

• A. ${10}^{-100}$
• B. $100$
• C. ${10}^{100}$
• D. $10$

Answer 1

The correct option is C ${10}^{100}$

Step: Find the multiplicative inverse of ${10}^{-100}$

Let $a$ be the multiplicative inverse of ${10}^{-100}$

So, $a\times {10}^{100}=1$

$\Rightarrow a=\frac{1}{{10}^{100}}$

$\Rightarrow a=\frac{1}{\frac{1}{{10}^{100}}}[\because a^{-m}=\frac{1}{a^m};(a\ne 0)]$

$\therefore a={100}^{100}$

So, the multiplicative inverse of ${10}^{-100}$ is ${10}^{100}$.

Hence, the correct option is (C).