Patrick W. answered • 10/30/16

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High School Mathematics Teacher, Passionate Math Geek

There are some useful rules for exponents:

(x^m)*(x^n)=x^(m+n)

(x^m)/(x^n)=x^(m-n)

(x^m)^n=x^(mn)

To help see how to use these rules, sometimes it's helpful to replace something in your expression with u.

In this case, I'm going to call u=x^(1/2):

x^(3/2)-u

But wait, there's another u in there! 3/2 can be written as the sum of 1+1/2, so I can use one of my rules:

x^(1+1/2)-u

(x^1)*(x^(1/2))-u

xu-u

u(x-1)

Now you can replace back in for u, and I think you'll be simplified!

(x-1)sqrt(x)