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Simplify. Assume all variables are positive.\newlinec114c114c^{\frac{11}{4}} \cdot c^{\frac{11}{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______\newline

Full solution

Q. Simplify. Assume all variables are positive.\newlinec114c114c^{\frac{11}{4}} \cdot c^{\frac{11}{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______\newline
  1. Identify and Apply Property: Identify the equation and apply the property of multiplying powers with the same base.\newlineWhen multiplying powers with the same base, we add the exponents.\newlinec114×c114=c114+114c^{\frac{11}{4}} \times c^{\frac{11}{4}} = c^{\frac{11}{4} + \frac{11}{4}}
  2. Add Exponents: Add the exponents. 114+114=224\frac{11}{4} + \frac{11}{4} = \frac{22}{4}
  3. Simplify Exponent: Simplify the exponent.\newline224\frac{22}{4} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newline224=(22÷2)(4÷2)=112\frac{22}{4} = \frac{(22 \div 2)}{(4 \div 2)} = \frac{11}{2}
  4. Write Final Answer: Write the final answer using the simplified exponent. c114×c114=c112c^{\frac{11}{4}} \times c^{\frac{11}{4}} = c^{\frac{11}{2}}

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