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Simplify. Assume all variables are positive. $\newline$ $\frac{v^{\frac{4}{3}}}{v^{\frac{2}{3}}}$ $\newline$ 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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{v^{\frac{4}{3}}}{v^{\frac{2}{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

______

Identify operation with exponents: We have the expression: $\newline$ $v^{\frac{4}{3}}/v^{\frac{2}{3}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply rule for dividing powers: Simplify the expression by subtracting the exponents. $\newline$ $v^{\frac{4}{3}}/v^{\frac{2}{3}}$ $\newline$ = $v^{\frac{4}{3} - \frac{2}{3}}$ $\newline$ = $v^{\frac{2}{3}}$

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