If $\left(2^{a}\right)\left(2^{b}\right)=64$, then the mean (average) of $a$ and $b$ is
(A) 12
(B) $\frac{5}{2}$
(C) $\frac{3}{2}$
(D) 3
(E) 8

Part B: Each correct answer is worth 6.
Since $\left(2^{a}\right)\left(2^{b}\right)=64$, then $2^{a+b}=64$, using an exponent law.

Since $64=2^{6}$, then $2^{a+b}=2^{6}$ and so $a+b=6$.

Therefore, the average of $a$ and $b$ is $\frac{1}{2}(a+b)=3$.

ANSWER: (D)