Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{4}{3}} \cdot r^{\frac{7}{3}}}{r^{\frac{5}{3}}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{r^{\frac{4}{3}} \cdot r^{\frac{7}{3}}}{r^{\frac{5}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Combine Exponents: Combine the exponents in the numerator using the property of exponents that states when you multiply like bases, you add the exponents. $\newline$ $r^{\frac{4}{3}} \times r^{\frac{7}{3}} = r^{\frac{4}{3} + \frac{7}{3}}$
Add Exponents: Add the exponents in the numerator. $\newline$ $\frac{4}{3} + \frac{7}{3} = \frac{11}{3}$ $\newline$ So, $r^{\frac{4}{3}} \times r^{\frac{7}{3}} = r^{\frac{11}{3}}$
Divide Like Bases: Divide the expression in the numerator by the expression in the denominator using the property of exponents that states when you divide like bases, you subtract the exponents. $\newline$ $\frac{r^{11/3}}{r^{5/3}} = r^{11/3 - 5/3}$
Subtract Exponents: Subtract the exponents. $\newline$ $\frac{11}{3} - \frac{5}{3} = \frac{6}{3}$ $\newline$ So, $\frac{r^{\frac{11}{3}}}{r^{\frac{5}{3}}} = r^{\frac{6}{3}}$
Simplify Exponent: Simplify the exponent. $6/3 = 2$ So, $r^{6/3} = r^2$