# How do you evaluate fractional exponents?

##### 1 Answer

You can just remember this rule, or you can learn about why this is:

**fractional exponent #1/b#**

So first we're going to look at an expression of the form:

To investigate what this means, we need to go from

What does multiplication mean? Repeated addition. So we can instead of multiplying by b, adding the number to itself

There is a rule you use when multiplying numbers with the same radical: add the exponents. If we reverse this rule, we get:

Now, we still know that this number is equal to

It's the bth-root of

For example:

If we multiply this by itself 3 times we get:

What number multiplied by itself 3 times, gives you 8.

It's of course

**What about #a/b#?**

To know what

Repeated multiplication is equal to exponentiation, so we can write:

You can also bring the exponent in the root: