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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, which states that when multiplying like bases, you add the exponents: c(a/b)×c(c/d)=c((a/b)+(c/d))c^{(a/b)} \times c^{(c/d)} = c^{((a/b) + (c/d))}.
  2. Add Exponents: Add the exponents (54)(\frac{5}{4}) and (94)(\frac{9}{4}) together: (54)+(94)=(5+94)=144(\frac{5}{4}) + (\frac{9}{4}) = (\frac{5 + 9}{4}) = \frac{14}{4}.
  3. Simplify Fraction: Simplify the fraction 144\frac{14}{4}, which reduces to 3.53.5 or 72\frac{7}{2} when written as an improper fraction.
  4. Write Final Answer: Write the final answer using the simplified exponent: c72c^{\frac{7}{2}}.

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