If $x^{2} y z^{3}=7^{4}$ and $x y^{2}=7^{5}$, then $x y z$ equals
(A) 7
(B) $7^{2}$
(C) $7^{3}$
(D) $7^{8}$
(E) $7^{9}$
Solution

By multiplying the given equations together we obtain

$$
\begin{aligned}
\left(x^{2} y z^{3}\right)\left(x y^{2}\right) & =\left(7^{4}\right)\left(7^{5}\right) \\
x^{3} y^{3} z^{3} & =7^{9}
\end{aligned}
$$

Taking the cube root of each side gives $x y z=7^{3}$.

ANSWER: (C)

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