If $x^{2} y z^{3}=7^{3}$ and $x y^{2}=7^{9}$, then $x y z$ equals
(A) $7^{10}$
(B) $7^{9}$
(C) $7^{8}$
(D) $7^{6}$
(E) $7^{4}$
Solution

Multiplying the given equations together yields

$$
\begin{aligned}
\left(x^{2} y z^{3}\right)\left(x y^{2}\right) & =\left(7^{3}\right)\left(7^{9}\right) \\
x^{3} y^{3} z^{3} & =7^{12}
\end{aligned}
$$

Taking the cube root of each side of the equation gives $x y z=7^{4}$.

ANSWER: (E)