What do you do if the base number is not a fraction but the exponent is a fraction?

Answer 1

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.