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Simplify. Assume all variables are positive.\newlines43s23s13\frac{s^{\frac{4}{3}}}{s^{\frac{2}{3}} \cdot s^{\frac{1}{3}}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______

Full solution

Q. Simplify. Assume all variables are positive.\newlines43s23s13\frac{s^{\frac{4}{3}}}{s^{\frac{2}{3}} \cdot s^{\frac{1}{3}}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
  1. Write Quotient Rule: Write down the expression and apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases, you subtract the exponents.\newlineExpression: s43/(s23s13)s^{\frac{4}{3}} / (s^{\frac{2}{3}} \cdot s^{\frac{1}{3}})
  2. Combine Exponents: Combine the exponents in the denominator using the product rule for exponents.\newlineThe product rule states that when multiplying like bases, you add the exponents.\newlines23×s13=s23+13=s33=s1s^{\frac{2}{3}} \times s^{\frac{1}{3}} = s^{\frac{2}{3} + \frac{1}{3}} = s^{\frac{3}{3}} = s^1
  3. Apply Quotient Rule: Now, apply the quotient rule to the expression from Step 11 using the simplified denominator from Step 22. \newlines43/s1=s4333=s13s^{\frac{4}{3}} / s^1 = s^{\frac{4}{3} - \frac{3}{3}} = s^{\frac{1}{3}}
  4. 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.\newlineFinal simplified expression: s13s^{\frac{1}{3}}

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