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Simplify. Assume all variables are positive.\newlinec12⋅c52c^{\frac{1}{2}} \cdot c^{\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______

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Q. Simplify. Assume all variables are positive.\newlinec12⋅c52c^{\frac{1}{2}} \cdot c^{\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 Equation and Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying powers with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinec12×c52=c12+52c^{\frac{1}{2}} \times c^{\frac{5}{2}} = c^{\frac{1}{2} + \frac{5}{2}}.
  2. Add Exponents: Add the exponents. 12+52=(1+5)2=62.\frac{1}{2} + \frac{5}{2} = \frac{(1 + 5)}{2} = \frac{6}{2}.
  3. Simplify Fraction: Simplify the fraction 62\frac{6}{2}. 62=3\frac{6}{2} = 3.
  4. Write Final Answer: Write the final answer using the simplified exponent.\newlinec12×c52=c3c^{\frac{1}{2}} \times c^{\frac{5}{2}} = c^3.

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