## Intermediate Algebra (12th Edition)

Since $\sqrt[3]{125}=5$, the expression, $\dfrac{\sqrt[3]{10}}{5}$ (Choice D), is equivalent to \begin{align*} & \dfrac{\sqrt[3]{10}}{\sqrt[3]{125}} .\end{align*} Since $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$, then the expression above is equivalent to \begin{align*}\require{cancel} & \sqrt[3]{\dfrac{10}{125}} \\\\&= \sqrt[3]{\dfrac{\cancelto2{10}}{\cancelto{25}{125}}} &(\text{divide by }5) \\\\&= \sqrt[3]{\dfrac{2}{25}} .\end{align*} Since $\sqrt[3]{\dfrac{2}{25}}\ne\sqrt[3]{\dfrac{2}{5}}$, then the expression that is not equal to $\sqrt[3]{\dfrac{2}{5}}$ is Choice D.