The product of a positive number, its square, and its reciprocal is $\frac{100}{81}$. What is the number?
(A) $\frac{81}{100}$
(B) $\frac{100}{81}$
(C) $\frac{9}{10}$
(D) $\frac{10}{9}$
(E) $\frac{10000}{6561}$
Solution

Let $x$ represent the number.

Then $x\left(x^{2}\right)\left(\frac{1}{x}\right)=\frac{100}{81}$

$$
\begin{aligned}
x^{2} & =\frac{100}{81} \\
x & = \pm \frac{10}{9}
\end{aligned}
$$

Since $x$ is positive, $x=\frac{10}{9}$.

ANSWER: (D)