What happens when you square a cubed root or cube a square root and problems like these. show examples.

Cube root of any value x means the power of or exponent of 1/3 of x.
X^1/3
if you square it,
the power of a power is multiplied according to exponent laws.
Hence,
===> (X^1/3)^2
         = X^2/3

Now,
Square root of any value x means the power of or exponent of 1/2 of x.
X^1/2
if you cube it,
the power of a power is multiplied according to exponent laws.
Hence,
===> (X^1/2)^3
         = X^3/2
Hope it helps