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Simplify. Assume all variables are positive. $\newline$ $v^{\frac{2}{7}} \cdot v^{\frac{8}{7}}$ $\newline$ 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

v^{\frac{2}{7}} \cdot v^{\frac{8}{7}}

\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 Rule: Identify the equation and apply the exponent rule for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $v^{\frac{2}{7}} \times v^{\frac{8}{7}} = v^{\frac{2}{7} + \frac{8}{7}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{2}{7} + \frac{8}{7} = \frac{2 + 8}{7} = \frac{10}{7}$ . $\newline$ So, $v^{\frac{2}{7}} \times v^{\frac{8}{7}} = v^{\frac{10}{7}}$ .
Write Final Answer: Write the final 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. $\newline$ The final answer is $v^{\frac{10}{7}}$ , which is already in the correct form.

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