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Simplify. Assume all variables are positive.\newlines94s74s^{\frac{9}{4}} \cdot s^{\frac{7}{4}}\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.\newlines94s74s^{\frac{9}{4}} \cdot s^{\frac{7}{4}}\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. Identify Equation: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlines94×s74=s94+74s^{\frac{9}{4}} \times s^{\frac{7}{4}} = s^{\frac{9}{4} + \frac{7}{4}}.
  2. Add Exponents: Add the exponents. 94+74=164\frac{9}{4} + \frac{7}{4} = \frac{16}{4}.
  3. Simplify Exponent: Simplify the exponent. 164=4\frac{16}{4} = 4.
  4. Write Final Answer: Write the final answer using the simplified exponent. s94×s74=s4.s^{\frac{9}{4}} \times s^{\frac{7}{4}} = s^{4}.

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