Fractional Exponents

Question

Can someone explain how I solve fractional exponents problems where a number is raised to a fraction power? For example

16^3/4

Answer 1

we can also write this problem as 16^3(1/4) We have factored out the 3 from the 3/4 leaving 1/4.  If you multiply 3 times 1/4 you get 3/4

Now that you have a whole number exponent you can take 16 cubed which give you

4096

so you have 4096^(1/4)

Then you can take the 4th root of 4096 which ends up as 8

 

To do this another way, You can start by taking the 4th root of 16 which is 2

raise that to the 3rd power

2^3=8

Either way you get the correct answer.  The key is to get a 1 in the numerator of the fraction by factoring out the whole number numerator.  Once you have that you can raise the number to the whole number power or you can take the root of the remaining fraction.  Either way is correct.