Question

How do you evaluate `2^(5/2) - 2^(3/2)`?

Answer 1

You can write them in a more "friendly" way using the fact that:
`x^(m/n)=rootn(x^m)` so you get:
`sqrt(2^5)-sqrt(2^3)=sqrt(2^2*2^2*2)-sqrt(2^2*2)=`
you can take out from the roots as many `2^2` you can (`sqrt(2^2)=2`):
`=2^2sqrt(2)-2sqrt(2)=`
collect the roots:
`=sqrt(2)[4-2]=2sqrt(2)`