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

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

w^{\frac{4}{3}} \times 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

______

\newline

Combine powers of w: Combine the powers of w by adding the exponents. $\newline$ When multiplying powers with the same base, we add the exponents according to the rule $a^m \cdot a^n = a^{m+n}$ . $\newline$ $w^{4/3} \cdot w^{7/3}$ $\newline$ $= w^{(4/3) + (7/3)}$ $\newline$ $= w^{(4+7)/3}$ $\newline$ $= w^{11/3}$

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