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Simplify. Assume all variables are positive.\newlinec54c94c^{\frac{5}{4}} \cdot c^{\frac{9}{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.\newlinec54c94c^{\frac{5}{4}} \cdot c^{\frac{9}{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 and Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinec54×c94=c54+94c^{\frac{5}{4}} \times c^{\frac{9}{4}} = c^{\frac{5}{4} + \frac{9}{4}}.
  2. Add Exponents: Add the exponents. 54+94=144.\frac{5}{4} + \frac{9}{4} = \frac{14}{4}.
  3. Simplify Exponent: Simplify the exponent. \newline144\frac{14}{4} can be simplified to 3.53.5 or 72\frac{7}{2}.\newlinec144=c72c^{\frac{14}{4}} = c^{\frac{7}{2}}.
  4. Write Final Answer: Write the final answer.\newlineThe simplified form of c5/4×c9/4c^{5/4} \times c^{9/4} is c7/2c^{7/2}.

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