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Simplify. Assume all variables are positive. $\newline$ $u^{\frac{4}{3}} \times u^{\frac{7}{3}}$ $\newline$ Write your answer in the form $A$ or $A/B$ , 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{4}{3}} \times u^{\frac{7}{3}}

\newline

Write your answer in the form

A

or

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 Exponents: Combine the powers of $u$ by adding the exponents. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $u^{\frac{4}{3}} \times u^{\frac{7}{3}} = u^{\left(\frac{4}{3} + \frac{7}{3}\right)}$
Add Exponents: Perform the addition of the exponents. $\newline$ $(\frac{4}{3}) + (\frac{7}{3}) = (\frac{4 + 7}{3}) = \frac{11}{3}$ $\newline$ So, $u^{\frac{4}{3}} \cdot u^{\frac{7}{3}} = u^{\frac{11}{3}}$
Ensure Positivity: Ensure that the exponent is positive. $\newline$ The exponent $\frac{11}{3}$ is already positive, so no further action is needed.

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