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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{8}{3}}}{w^{\frac{2}{3}}}$ $\newline$ 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{w^{\frac{8}{3}}}{w^{\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

______

Write Expression: Write down the given expression. $\newline$ We have the expression $w^{\frac{8}{3}}/w^{\frac{2}{3}}$ . $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply Exponent Rule: Apply the exponent rule for division. $\newline$ $w^{\frac{8}{3}}/w^{\frac{2}{3}} = w^{\frac{8}{3} - \frac{2}{3}}$ $\newline$ Perform the subtraction of the exponents. $\newline$ $w^{\frac{8}{3} - \frac{2}{3}} = w^{\frac{6}{3}}$
Simplify Exponent: Simplify the exponent. $\newline$ $w^{\frac{6}{3}} = w^2$ $\newline$ Since $6$ divided by $3$ equals $2$ , the expression simplifies to $w^2$ .

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