Can you find the cube root of negative numbers, like the cube root of -64? explain why or why not.

Yes

remember that an odd power of a negative is negative
(-1)(-1)(-1)=(-1) tiat is negative
alsoo remember that ∛(ab)=(∛a)(∛b)

so
∛(-64)=(∛-1)(∛64)=(-1)(4)=-4