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Simplify. Assume all variables are positive.\newlinec74c54c^{\frac{7}{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.\newlinec74c54c^{\frac{7}{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 and Apply 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}.\newlinec74×c54=c74+54c^{\frac{7}{4}} \times c^{\frac{5}{4}} = c^{\frac{7}{4} + \frac{5}{4}}.
  2. Add Exponents: Add the exponents.\newline74+54=(7+5)4=124\frac{7}{4} + \frac{5}{4} = \frac{(7+5)}{4} = \frac{12}{4}.
  3. Simplify Fraction: Simplify the fraction 124\frac{12}{4}. 124=3\frac{12}{4} = 3.
  4. Write Final Expression: Write the final expression using the simplified exponent. c74×c54=c3c^{\frac{7}{4}} \times c^{\frac{5}{4}} = c^3.

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