Simplify. Assume all variables are positive. s^(4/3)/(s^(2/3) * s^(1/3)) Write your answer in the form A or 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. ______

Write Quotient Rule: Write down the expression and apply the quotient rule for exponents. The quotient rule states that when dividing like bases, you subtract the exponents. Expression: s^(4/3) / (s^(2/3) * s^(1/3))Combine Exponents: Combine the exponents in the denominator using the product rule for exponents. The product rule states that when multiplying like bases, you add the exponents. s^(2/3) * s^(1/3) = s^(2/3 + 1/3) = s^(3/3) = s^1Apply Quotient Rule: Now, apply the quotient rule to the expression from Step 1 using the simplified denominator from Step 2. s^(4/3) / s^1 = s^(4/3 - 3/3) = s^(1/3)Final Simplified Expression: Since all exponents are positive and there are no variables in common in the numerator and denominator, the expression is already in the simplest form. Final simplified expression: s^(1/3)

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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{4}{3}}}{s^{\frac{2}{3}} \cdot s^{\frac{1}{3}}}$ $\newline$ 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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Algebra 2

Simplify radical expressions with variables II

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Q. Simplify. Assume all variables are positive.

\newline

\frac{s^{\frac{4}{3}}}{s^{\frac{2}{3}} \cdot s^{\frac{1}{3}}}

\newline

Write your answer in the form

A

\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 Quotient Rule: Write down the expression and apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing like bases, you subtract the exponents. $\newline$ Expression: $s^{\frac{4}{3}} / (s^{\frac{2}{3}} \cdot s^{\frac{1}{3}})$
Combine Exponents: Combine the exponents in the denominator using the product rule for exponents. $\newline$ The product rule states that when multiplying like bases, you add the exponents. $\newline$ $s^{\frac{2}{3}} \times s^{\frac{1}{3}} = s^{\frac{2}{3} + \frac{1}{3}} = s^{\frac{3}{3}} = s^1$
Apply Quotient Rule: Now, apply the quotient rule to the expression from Step $1$ using the simplified denominator from Step $2$ . $\newline$ $s^{\frac{4}{3}} / s^1 = s^{\frac{4}{3} - \frac{3}{3}} = s^{\frac{1}{3}}$
Final Simplified Expression: Since all exponents are positive and there are no variables in common in the numerator and denominator, the expression is already in the simplest form. $\newline$ Final simplified expression: $s^{\frac{1}{3}}$