What rules are for a product of negative numbers under same exponent?

Question

Though it is a really simple question, I am stuck in explaining myself where I break the rules. $$\sqrt{-3}\sqrt{-3} = i^2\sqrt{9}=-3=(-3)^{\frac{1}{2}}(-3)^{\frac{1}{2}} = (-3)^{\frac{1}{2}+\frac{1}{2}}=-3$$ but in the next one, there's something wrong and I do not understand what it is: $$(-3)^\frac{1}{2}(-3)^\frac{1}{2}=((-3)(-3))^\frac{1}{2}=\sqrt{9}=3$$ That is, why cannot I get the product of the bases since I have the same exponent?