If $2^{a} 3^{b}=8\left(6^{10}\right)$, where $a$ and $b$ are integers, then $b-a$ equals
(A) 0
(B) 23
(C) -13
(D) -7
(E) -3
We rewrite the right side using exponent laws:

$$
\begin{aligned}
2^{a} 3^{b} & =8\left(6^{10}\right) \\
& =2^{3}\left([(2)(3)]^{10}\right) \\
& =2^{3}\left(2^{10} 3^{10}\right) \\
& =2^{13} 3^{10}
\end{aligned}
$$

and so $a=13$ and $b=10$, which tells us that $b-a=-3$.

ANSWER: (E)