Simplify. Assume all variables are positive. $\newline$ $r^{\frac{1}{3}} \cdot r^{\frac{4}{3}}$ $\newline$ 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

r^{\frac{1}{3}} \cdot r^{\frac{4}{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

______

Identify expression: Identify the expression to be simplified. $\newline$ We have the expression $r^{1/3} \times r^{4/3}$ and we need to simplify it.
Apply product rule: Apply the product rule for exponents. $\newline$ The product rule states that when multiplying two powers with the same base, you add the exponents. So, we add the exponents $\frac{1}{3}$ and $\frac{4}{3}$ . $\newline$ $r^{\frac{1}{3}} \times r^{\frac{4}{3}} = r^{\frac{1}{3} + \frac{4}{3}}$
Perform exponent addition: Perform the addition of the exponents. $\newline$ $\frac{1}{3} + \frac{4}{3} = \frac{5}{3}$ $\newline$ So, $r^{\frac{1}{3}} \times r^{\frac{4}{3}} = r^{\frac{5}{3}}$
Write final expression: Write the final simplified expression. $\newline$ The expression $r^{1/3} \times r^{4/3}$ simplifies to $r^{5/3}$ .