1. ## Square root help!

I'm in the middle of solving a difficult calculus problem and unfortunately it's been years since I've taken math. I'm trying to simplify an equation and I can't seem to remember what the different ways to write square root are. I know that the square root of x can be written as x^(1/2).

What is another way to write x^(3/2)? Is it the same as 3*x^(1/2)?

2. Remember that $\displaystyle x^{\frac{a}{b}} = \sqrt[b]{x^a}$. Sometimes is useful as well write $\displaystyle x^{\frac{a}{b}}$ as $\displaystyle (x^{a})^{\frac{1}{b}}$.
When you take the derivative of a function like this you should use the general formula: $\displaystyle \dfrac{d}{dx}x^{\frac{a}{b}} = \dfrac{a}{b}\cdot x^{(\frac{a}{b}-1)}$.

3. Well, here's the real problem. I'm trying to simplify this equation and I'm completely stuck. I have [-(9-t^2)^(1/2)] + [(t^2)/[(9-(t^2))^(3/2)] all divided by (9-(t^2)).

My book says that somehow this simplifies to 1+ 9/[(9-(t^2)]^(3/2) . If you could help me simplify this by any chance that would be awesome!