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Simplify. Assume all variables are positive. $\newline$ $c^{\frac{11}{6}} \cdot c^{\frac{13}{6}}$ $\newline$ 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

c^{\frac{11}{6}} \cdot c^{\frac{13}{6}}

\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: $a^m \times a^n = a^{m+n}$ . $\newline$ $c^{\frac{11}{6}} \times c^{\frac{13}{6}} = c^{\left(\frac{11}{6} + \frac{13}{6}\right)}$ .
Add Exponents: Add the exponents $(\frac{11}{6})$ and $(\frac{13}{6})$ . $\frac{11}{6} + \frac{13}{6} = \frac{11 + 13}{6} = \frac{24}{6}$ .
Simplify Fraction: Simplify the fraction $24/6$ . $24/6 = 4$ .
Write Final Expression: Write the final simplified expression using the simplified exponent. $c^{\frac{24}{6}} = c^4$ .

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