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Simplify. Assume all variables are positive. $\newline$ $r^{\frac{5}{2}} \cdot r^{\frac{5}{2}}$ $\newline$ 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

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Q. Simplify. Assume all variables are positive.

\newline

r^{\frac{5}{2}} \cdot r^{\frac{5}{2}}

\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 and Apply Property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $r^{\frac{5}{2}} \times r^{\frac{5}{2}} = r^{\left(\frac{5}{2} + \frac{5}{2}\right)}$ .
Perform Exponent Addition: Perform the addition of the exponents. $(\frac{5}{2}) + (\frac{5}{2}) = \frac{10}{2}$ .
Simplify Fraction: Simplify the fraction $\frac{10}{2}$ . $\frac{10}{2} = 5$ .
Write Final Expression: Write the final expression using the simplified exponent. $r^{\frac{5}{2}} \times r^{\frac{5}{2}} = r^5$ .

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