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Simplify. Assume all variables are positive. $\newline$ $u^{\frac{17}{6}} \cdot u^{\frac{17}{6}}$ $\newline$ 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

u^{\frac{17}{6}} \cdot u^{\frac{17}{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 Equation 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: $\newline$ $u^{\frac{a}{b}} \times u^{\frac{c}{d}} = u^{\left(\frac{a}{b} + \frac{c}{d}\right)}$ $\newline$ So, $u^{\frac{17}{6}} \times u^{\frac{17}{6}}$ becomes $u^{\left(\frac{17}{6} + \frac{17}{6}\right)}$ .
Add Exponents: Add the exponents. $u^{\frac{17}{6} + \frac{17}{6}}$ is $u^{\frac{34}{6}}$ .
Simplify Exponent: Simplify the exponent. $\frac{34}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\frac{34}{6}$ simplifies to $\frac{17}{3}$ .
Write Final Answer: Write the final answer. $\newline$ The simplified form is $u^{\frac{17}{3}}$ .

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