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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 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: \newlineam×an=a(m+n)a^m \times a^n = a^{(m+n)}\newlineSo, c54×c54c^{\frac{5}{4}} \times c^{\frac{5}{4}} becomes c54+54c^{\frac{5}{4} + \frac{5}{4}}.
  2. Add Exponents: Add the exponents. 54+54\frac{5}{4} + \frac{5}{4} equals 104\frac{10}{4}.
  3. Simplify Exponent: Simplify the exponent. 104\frac{10}{4} can be simplified to 52\frac{5}{2} because both the numerator and the denominator are divisible by 22.
  4. Write Final Answer: Write the final answer using the simplified exponent.\newlineThe expression c5/4×c5/4c^{5/4} \times c^{5/4} simplifies to c5/2c^{5/2}.

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