Question

Find the value of ${100}^{\frac{5}{2}}÷{100}^{-\frac{1}{2}}$.

• A. ${10}^2$
• B. ${10}^6$
• C. ${10}^{-6}$
• D. ${10}^4$

Answer 1

The correct option is B ${10}^6$

${100}^{\frac{5}{2}}÷{100}^{-\frac{1}{2}}={100}^{\frac{5}{2}-(-\frac{1}{2})(\because \frac{a^m}{a^n}=a^{m-n})}={100}^{\frac{6}{2}}={100}^3=({10}^2{)}^3={10}^6[(a^b{)}^m=a^{bm}]$
$\therefore ({100}^{\frac{5}{2}}÷{100}^{-\frac{1}{2}})={10}^6$