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Simplify. Assume all variables are positive.\newlinec52c52c^{\frac{5}{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______

Full solution

Q. Simplify. Assume all variables are positive.\newlinec52c52c^{\frac{5}{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 and Apply Property: Identify the equation and apply the product of powers property.\newlineThe product of powers property states that when you multiply two powers with the same base, you add the exponents: am×an=a(m+n)a^m \times a^n = a^{(m+n)}.\newlinec(5/2)×c(5/2)=c((5/2)+(5/2))c^{(5/2)} \times c^{(5/2)} = c^{((5/2) + (5/2))}.
  2. Add Exponents: Add the exponents.\newline(52)+(52)=102(\frac{5}{2}) + (\frac{5}{2}) = \frac{10}{2}.
  3. Simplify Fraction: Simplify the fraction 102\frac{10}{2}. 102=5\frac{10}{2} = 5.
  4. Write Final Answer: Write the final answer using the simplified exponent. c102=c5c^{\frac{10}{2}} = c^5.

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