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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{1}{3}}}{s^{\frac{5}{3}}}$ $\newline$ 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 II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{s^{\frac{1}{3}}}{s^{\frac{5}{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

______

Subtract Exponents: Write $s^{1/3}/s^{5/3}$ as a single power of $s$ by subtracting the exponents. $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $s^{1/3}/s^{5/3}$ $\newline$ = $s^{(1/3)-(5/3)}$ $\newline$ = $s^{-4/3}$
Negative Exponent Rule: Express $s^{-\frac{4}{3}}$ with a positive exponent. $\newline$ According to the negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $s^{-\frac{4}{3}} = \frac{1}{s^{\frac{4}{3}}}$

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