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Simplify. Assume all variables are positive.\newlines32s52s^{\frac{3}{2}} \cdot s^{\frac{5}{2}}\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.\newlines32s52s^{\frac{3}{2}} \cdot s^{\frac{5}{2}}\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 Expression: Identify the expression to simplify.\newlineWe have the expression s32s52s^{\frac{3}{2}} \cdot s^{\frac{5}{2}} and we need to simplify it.
  2. Apply Property of Exponents: Apply the property of exponents for multiplying with the same base.\newlineWhen multiplying expressions with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.
  3. Add Exponents: Add the exponents.\newlines32×s52=s32+52=s82s^{\frac{3}{2}} \times s^{\frac{5}{2}} = s^{\frac{3}{2} + \frac{5}{2}} = s^{\frac{8}{2}}.
  4. Simplify Exponent: Simplify the exponent. s82=s4s^{\frac{8}{2}} = s^4.
  5. Write Final Answer: Write the final answer.\newlineThe simplified form of the expression is s4s^4.

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