Answer
$14 \sqrt[3] {3}$
Work Step by Step
In this subtraction problem, the indices are the same, but the radicands are different.
We need to transform the radicand so that they are the same. Rewrite the radicands as the products of at least one cube so that we can take some out of the radical later:
$=10 \sqrt[3] {(3)^3(3)} - 8 \sqrt[3] {[(2)^3](3)}$
Take the cube roots of anything raised to the power of $3$ within the radicand:
$=10(3) \sqrt[3] {3} - 8(2) \sqrt[3] {3}$
$=30 \sqrt[3] {3} - 16 \sqrt[3] {3}$
The radicals are now similar so subtract to obtain:
$=(30-16)\sqrt[3]{3}\\
=14 \sqrt[3] {3}$
