I'm wondering if you could call this a "simplification" but here it is "rewritten" in another form:
since $$32=2\times2\times2\times2\times2=2^5$$,
we can write:
$$\sqrt[3]{32}= \sqrt[3]{2^5} = 2^{\frac53}$$
(because $$\sqrt[3]{x}= x^{\frac13}$$)
or if one absolutely wants to get some integer out of the root, we could write:
$$\sqrt[3]{32} = \sqrt[3]{8\times4}= \sqrt[3]{2^3\times4} = 2 \sqrt[3]{4}$$