Q:  What does it mean when you have a fraction as an exponent?

A:  Firstly, we must be familiar with the following: X^a/b = ^b√X^a

When rewriting, think of a fractional exponent as a “tree”. The top number is the number of branches (how many multiples of X there are) and the bottom number is the root.

It is often important to rewrite radicals (√) as fractional exponents. A calculator does not necessarily have the right buttons to type ⁵√9⁶, but you could instead type in 9^6/5 to get an answer.

Being able to go back and forth between fractional form and radical form is critical!

Example:

Q: Compute (without a calculator): 64^2/3

A: Rewrite and simplify: 64^2/3 = ³√64² = (³√64)² = 4² = 16!