Answer
Simplify the expression $\frac{27a^{\frac{5}{2}}b^{\frac{4}{3}}}{9a^2b}$
Answer: $3a^{\frac{1}{2}}b^{\frac{1}{3}}$
Work Step by Step
Simplify $\frac{27a^{\frac{5}{2}}b^{\frac{4}{3}}}{9a^2b}$
1. Divide the numbers $\frac{27}{9}=3$
2. Simplify: $\frac{3a^{\frac{5}{2}}b^{\frac{4}{3}}}{a^2b}$
3. Apply exponent rule:$\quad \frac{x^a}{x^b}\:=\:x^{a-b}$
4. Simplify: $\frac{3a^{\frac{1}{2}}b^{\frac{4}{3}}}{b}$
5. Apply the exponent rule: $\frac{x^a}{x^b}=x^{a-b}$
6. Simplify: $3a^{\frac{1}{2}}b^{\frac{1}{3}}$
