Question

Match the following exponents with their simplified form

• A. $4^{-1}$
• B. $4$
• C. $4^2$

Answer 1

A. ${64}^{\frac{2}{3}}=(4^3{)}^{\frac{2}{3}}=4^{3\times \frac{2}{3}}=4^2$
$(\because (a^m{)}^n=a^{mn})$

B. ${64}^{\frac{1}{3}}=(4^3{)}^{\frac{1}{3}}=4^{3\times \frac{1}{3}}=4$
$(\because (a^m{)}^n=a^{mn})$

C. ${64}^{-\frac{1}{3}}=(4^3{)}^{-\frac{1}{3}}=4^{-3\times \frac{1}{3}}=4^{-1}$
$(\because (a^m{)}^n=a^{mn})$