Question

The value of $(2^2{)}^{-3}$ is ___.

• A. $32$
• B. $\frac{1}{64}$
• C. $\frac{1}{2}$
• D. $256$

Answer 1

The correct option is B $\frac{1}{64}$

Using the law of exponents $(a^m{)}^n=a^{mn}$ where $a$ is a non-zero integer, $m$ and $n$ are any integers, we have
$(2^2{)}^{-3}=2^{(2\times -3)}=2^{-6}$
But we have $a^{-m}=\frac{1}{a^m}.$
$⟹(2^2{)}^{-3}=2^{-6}=\frac{1}{2^6}=\frac{1}{64}.$