Answer
$\dfrac{x\sqrt[3]{2}-\sqrt[3]{5}}{x^3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Simplify each term in the given expression, $
\sqrt[3]{\dfrac{2}{x^6}}-\sqrt[3]{\dfrac{5}{x^9}}
.$ Then make the terms similar (same denominator) to combine the numerators.
$\bf{\text{Solution Details:}}$
Simplifying each term of the expression above results to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{1}{x^6}\cdot2}-\sqrt[3]{\dfrac{1}{x^9}\cdot5}
\\\\=
\sqrt[3]{\left(\dfrac{1}{x^2}\right)^3\cdot2}-\sqrt[3]{\left(\dfrac{1}{x^3}\right)^3\cdot5}
\\\\=
\dfrac{1}{x^2}\sqrt[3]{2}-\dfrac{1}{x^3}\sqrt[3]{5}
\\\\=
\dfrac{\sqrt[3]{2}}{x^2}-\dfrac{\sqrt[3]{5}}{x^3}
.\end{array}
To simplify the expression above, make the terms similar by multiplying the necessary term/s to an expression equal to $1$. Hence, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{2}}{x^2}\cdot\dfrac{x}{x}-\dfrac{\sqrt[3]{5}}{x^3}
\\\\=
\dfrac{x\sqrt[3]{2}}{x^3}-\dfrac{\sqrt[3]{5}}{x^3}
.\end{array}
To combine similar terms, add/subtract the numerators and copy the similar denominator. Hence, the expression above is equivalent to \begin{array}{l}\require{cancel}
\dfrac{x\sqrt[3]{2}-\sqrt[3]{5}}{x^3}
.\end{array}
