Answer
$2x^2$
Work Step by Step
Before we can subtract these two numbers, we must transform them so that the radicals are the same. Only then can we perform the operation we are asked to do.
Let's expand the radicands into their constituent factors in both radicals. We want one of the factors to be a perfect square so that we can take it out from under the radical sign.
In the first radicand, the number $125$ is a perfect cube; in the second radicand, the number $27$ is also a perfect cube. The $x^6$ factors are also perfect cubes. Let's rewrite this problem so that we can see the perfect cubes easily:
$\sqrt[3] {(5^3)(x^2)^3} - \sqrt[3] {(3^3)(x^2)^3}$
Let's take the perfect cubes out from under the radical sign:
$5x^2 - 3x^2$
Now that the radicals are gone, we have two exponents with the same bases and powers, so we can just subtract:
$2x^2$
