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Simplify. Assume all variables are positive. $\newline$ $v^{\frac{7}{3}} \cdot v^{\frac{8}{3}}$ $\newline$ 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

v^{\frac{7}{3}} \cdot v^{\frac{8}{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 of $v$ : Combine the powers of $v$ by adding the exponents. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $v^{7/3} \times v^{8/3} = v^{(7/3) + (8/3)}$
Perform exponent addition: Perform the addition of the exponents. $\newline$ $(\frac{7}{3}) + (\frac{8}{3}) = (\frac{7 + 8}{3})$ $\newline$ $= \frac{15}{3}$
Write result as single power: Write the result as a single power of $v$ . $v^{\frac{15}{3}} = v^5$

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