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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{7}{3}}}{s^{\frac{4}{3}}}$ $\newline$ 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{s^{\frac{7}{3}}}{s^{\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 Expression: We have the expression: $\newline$ $\frac{s^{\frac{7}{3}}}{s^{\frac{4}{3}}}$ $\newline$ 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: $s^{\frac{7}{3}}/s^{\frac{4}{3}} = s^{\frac{7}{3} - \frac{4}{3}}$ Perform the subtraction of the exponents. $s^{\frac{7}{3} - \frac{4}{3}} = s^{\frac{3}{3}}$
Simplify Exponent: Simplify the exponent: $s^{\frac{3}{3}} = s^1$ Since any number raised to the power of $1$ is the number itself, we have: $s^1 = s$

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