What do you do if the base number is not a fraction but the exponent is a fraction?
Consider have x^(p/q)
where the base, x, is a whole number. p and q are also whole
numbers (q is not 0) so that the exponent, p/q, is a fraction.
Then
x^(p/q) = (x^p)^(1/q), that is, the qth root of x^p
or equivalently,
x^(p/q) = [x^(1/q)]^p, that is, the pth power of the qth root of
x.
For example,
64^(2/3) = 3rd root of 64^2 = 3rd [cube] root of 4096 = 16
or
(cube root of 64)^2 = 4^2 = 16.
If p/q is negative, the answer is the reciprocal of the answer
obtained with positive p/q.