Question

The multiplicative inverse of ${10}^4$ is.

• A. ${10}^{-2}$
• B. ${10}^{-4}$
• C. ${10}^{-1}$
• D. ${10}^{-3}$

Answer 1

The correct option is B ${10}^{-4}$

$a^{-m}$ is the multiplicative inverse of $a^m$, if $a^m\times a^{-m}=1$ (law of exponent)
Let's assume its multiplicative inverse is: $x$
Using above equation,
${10}^4\times x=1$
$\Rightarrow x=\frac{1}{{10}^4}$
$\Rightarrow x={10}^{-4}$