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Simplify. Assume all variables are positive. $\newline$ $u^{\frac{1}{3}} \cdot u^{\frac{1}{3}}$ $\newline$ 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 II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

u^{\frac{1}{3}} \cdot u^{\frac{1}{3}}

\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

______

Combine Powers with Same Base: Combine the powers of $u$ with the same base by adding the exponents. $\newline$ When multiplying powers with the same base, we add the exponents according to the rule: $a^m \times a^n = a^{m+n}$ . $\newline$ $u^{\frac{1}{3}} \times u^{\frac{1}{3}} = u^{\frac{1}{3} + \frac{1}{3}}$
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ $\newline$ So, $u^{\frac{1}{3}} \times u^{\frac{1}{3}} = u^{\frac{2}{3}}$
Write Final Answer: Write the final answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ have no variables in common and all exponents are positive. $\newline$ The final answer is $u^{\frac{2}{3}}$ , which is already in the correct form.

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