**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}√9^{6}, 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}√64^{2} = (^{3}√64)^{2} = 4^{2} = 16!

I know you haven’t posted in a while, but I just wanted to point out that 9^(5/6) = the sixth root of 9 to the fifth power, not the other way around.

You are exactly right – a typo on my end. I have fixed it!