Question

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

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

Answer 1

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

Let 𝑎 be the multiplicative inverse of ${10}^{–100}$
So, 𝑎 × ${10}^{-100}$ = 1
⟹ 𝑎=$\frac{1}{{10}^{-100}}$
⟹ 𝑎=${10}^{100}$
[∵ $a^{-m}$ =$\frac{1}{a^m}$ ; (𝑎 ≠0 )]
∴ 𝑎 = ${10}^{100}$
So, the multiplicative inverse of ${10}^{-100}$ is ${10}^{100}$.
Hence, the correct option is (C).