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Simplify. Assume all variables are positive.\newlinec54c54c^{\frac{5}{4}} \cdot c^{\frac{5}{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.\newlinec54c54c^{\frac{5}{4}} \cdot c^{\frac{5}{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: \newlinec54×c54=c54+54c^{\frac{5}{4}} \times c^{\frac{5}{4}} = c^{\frac{5}{4} + \frac{5}{4}}.
  2. Add Exponents: Perform the addition of the exponents. 54+54=104\frac{5}{4} + \frac{5}{4} = \frac{10}{4}.
  3. Simplify Exponent: Simplify the exponent. 104\frac{10}{4} can be simplified to 52\frac{5}{2} because 1010 divided by 44 is the same as 55 divided by 22.
  4. Write Final Answer: Write the final answer using the simplified exponent. c52c^{\frac{5}{2}} is the simplified form of the original expression.

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