Once you understand how to simplify square roots like , it's only a short step to simplifying expressions like .

The first step, as with square roots, is to find the prime factorization of 54, and then rewrite the cube root:

=

Now, we recognize that x has an exponent that's greater than 3, but is not a multiple of three. So we're going to rewrite it as a product of two factors, one of which is a perfect cube:

x⁴ = x³ · x¹

This means:

= =
 · =
3x

Let's try another. Simplify

Again, we do a prime factorization on 64:

=

We have several exponents greater than 5, so we need to do some rewriting:

= 
 · = 
2xz²

1.

Simplify

2.

Simplify

3.

Simplify

4.

Simplify

5.

Simplify