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Simplify. Assume all variables are positive. $\newline$ $w^{\frac{4}{3}} \cdot w^{\frac{7}{3}}$ $\newline$ 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

w^{\frac{4}{3}} \cdot w^{\frac{7}{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 and Apply Property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying powers with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $w^{\frac{4}{3}} \times w^{\frac{7}{3}} = w^{\frac{4}{3} + \frac{7}{3}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{4}{3} + \frac{7}{3} = \left(4 + 7\right) / 3 = \frac{11}{3}$ . $\newline$ So, $w^{\frac{4}{3}} \times w^{\frac{7}{3}} = w^{\frac{11}{3}}$ .
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 $w^{\frac{11}{3}}$ , which is already in the correct form.

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