How do you simplify fractions with indices like 16 and negative 3over2?

Answer 1

A negative index is the positive index applied to the reciprocal. So, 16^(-3/2) = (1/16)^(3/2)

The denominator of a fractional index represents the relevant root.

Thus, (1/16)^(3/2) = {sqrt(1/16)}3

Now, sqrt(1/16) = sqrt(1)/sqrt(16) = 1/4

So the given number is {1/4}^3 = 1/64.