Factor the following expression

3x^(3/2) - 9x^(1/2) + 6x^(-1/2)

= 3x^(-1/2)(x^2-3x+2)
=3x^(-1/2)(x-2)(x-1)

When you factor, like 4x^3-7x^2, you factor out the smallest power of x that is shared.
So when there are negative exponents, factor out the smallest.

The 3, -9, and 6 have a gcf of 3
Then the smallest power of x is x^-1/2

Now when you factor out x^-1/2 from x^ 3/2, 3/2-(-1/2)= 4/2=2, so x^2 is left.
Likewise when you factor x^-1/2 from x^1/2, 1/2-(-1/2)= 1, so x^1 is left.

So 3x^(-1/2)[x^2-3x+2] is the factored gcf

Now, the trinomial factors again

3x^(-1/2)[(x-2)(x-1)

Hoping that helps!

x^(1/2)(3x^(3/2) - 9x^(1/2) + 6x^(- 1/2)

3x^2 - 9x + 6

3)x^2 - 3 + 2)

3(x - 2)(x - 1)