How do you evaluate fractional exponents?
You can just remember this rule, or you can learn about why this is:
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
If we multiply this by itself 3 times we get:
What number multiplied by itself 3 times, gives you 8.
It's of course
To know what
Repeated multiplication is equal to exponentiation, so we can write:
You can also bring the exponent in the root: