# Fractional Exponents

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

A:  Firstly, we must be familiar with the following: Xa/b = b√Xa

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 96/5 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): 642/3

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

## 2 thoughts on “Fractional Exponents”

1. desertdweller says:

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.

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2. themathblogger says:

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

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