Question

Find the value of $m$ for which: ${100}^m÷{100}^4={100}^8$

• A. $1$
• B. $2$
• C. $3$
• D. $12$

Answer 1

Answer: (D)

$12$

${100}^m÷{100}^4={100}^{m-4}$

Now, we know that $\frac{a^m}{a^n}=a^{m-n}$
$\therefore m-4=8$
$\therefore m=12$
Upon, verifying, ${100}^{12}÷{100}^4={100}^{12-4}={100}^8$

So, option $D$ is correct.