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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

c^{\frac{13}{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 Exponent Rule: Identify the equation and apply the exponent multiplication property. $\newline$ When multiplying two exponents with the same base, we add the exponents: $\newline$ $a^m \times a^n = a^{(m+n)}$ $\newline$ So, $c^{\frac{13}{6}} \times c^{\frac{13}{6}}$ becomes $c^{\frac{13}{6} + \frac{13}{6}}$ .
Add Exponents: Add the exponents. $\frac{13}{6} + \frac{13}{6}$ equals $\frac{26}{6}$ when we add the numerators and keep the denominator the same.
Simplify Exponent: Simplify the exponent. $\frac{26}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\frac{26}{6}$ simplifies to $\frac{13}{3}$ .
Write Final Answer: Write the final answer. $\newline$ The simplified form of $c^{\frac{13}{6}} \times c^{\frac{13}{6}}$ is $c^{\frac{13}{3}}$ .

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