Question

If m is a positive integer which of the following is not equal to $(2^4{)}^m$?

• A. $2^{4m}$
• B. $4^{2m}$
• C. $2^m\left(2^{3m}\right)$
• D. $4^m\left(2^m\right)$

Answer 1

The correct option is D $4^m\left(2^m\right)$

${\left(2^4\right)}^m=2^{4m}$
$4^{2m}={\left(2^2\right)}^{2m}=2^{4m};$
$2^m\left(2^{3m}\right)=2^{m+3m}=2^{4m};$
$4^m\left(2^m\right)={\left(2^2\right)}^m{.2}^m=2^{2m}{.2}^m=2^{3m}\ne 2^{4m}$