Please help me out; factor and simplify x^(3/2)-x^(1/2)

Question

factor and simplify x^(3/2)-x^(1/2)

Answer 1

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)