How do you raise a number to an exponent that is a fraction?

Answer 1

You carry the exponent to the numerator and denominator. If the fraction is (m/n), then (m/n)x = (mx)/(nx)

For example: (3/4)2 = (32)/(42) = 9/16

If you meant that the exponent is a fraction, such as 82/3, then the denominator of the fractional exponent means to take the root (in the example, cube root) of the number, then the numerator means to take to the power (in the example, squared). You can do either operation first.

82/3 = ((8)2)1/3 = cube root(64) = 4, or ((8)1/3)2 = (2)2 = 4