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Simplify. Assume all variables are positive. $\newline$ $r^{\frac{8}{7}} \cdot r^{\frac{10}{7}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

r^{\frac{8}{7}} \cdot r^{\frac{10}{7}}

\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

______

Identify Equation & Apply Rule: Identify the equation and apply the exponent multiplication rule. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ So, $r^{\frac{8}{7}} \times r^{\frac{10}{7}} = r^{\frac{8}{7} + \frac{10}{7}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{8}{7} + \frac{10}{7} = \frac{(8 + 10)}{7} = \frac{18}{7}$ . $\newline$ So, $r^{\frac{8}{7}} \times r^{\frac{10}{7}} = r^{\frac{18}{7}}$ .
Write Final Answer: Write the final 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. $\newline$ The final answer is $r^{\frac{18}{7}}$ , which is already in the correct form.

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