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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{1}{3}}}{w^{\frac{4}{3}}}$ $\newline$ 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{1}{3}}}{w^{\frac{4}{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: We have the expression: $\newline$ $w^{\frac{1}{3}}/w^{\frac{4}{3}}$ $\newline$ Which operation will be applied with exponent? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply Exponent Rule: Apply the exponent rule for division: $w^{\frac{1}{3}}/w^{\frac{4}{3}}$ Simplify the expression by subtracting the exponents. $w^{\frac{1}{3} - \frac{4}{3}}$ $w^{-\frac{3}{3}}$ $w^{-1}$
Simplify Expression: Since we want the exponent to be positive, we can rewrite the expression as: $\newline$ $w^{-1} = \frac{1}{w^1}$ $\newline$ So the expression simplifies to: $\newline$ $\frac{1}{w}$

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