Simplify $\dfrac{x^3x^{-2}}{x^{5/2}\sqrt{x^9}}$. Your answer must have no negative exponents.
• This is just repeated use of the following rules: $x^a x^b=x^{a+b}$, $\frac{x^a}{x^b}=x^{a-b}$ and $(x^a)^b =x^{a b}$ for real numbers $a,b$. Recall also that $\sqrt{x}=x^{1/2}$. – Stefan Hansen Dec 9 '13 at 10:06
Hint: $a^m\cdot a^n=a^{n+m}$ and $\sqrt(x^m)=x^{\frac{m}{2}}$