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Simplify. Assume all variables are positive.\newliner54r74r^{\frac{5}{4}} \cdot r^{\frac{7}{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.\newliner54r74r^{\frac{5}{4}} \cdot r^{\frac{7}{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}.\newliner54×r74=r54+74r^{\frac{5}{4}} \times r^{\frac{7}{4}} = r^{\frac{5}{4} + \frac{7}{4}}.
  2. Add Exponents: Add the exponents.\newline54+74=(5+7)4\frac{5}{4} + \frac{7}{4} = \frac{(5 + 7)}{4}.
  3. Perform Addition: Perform the addition. 5+7=125 + 7 = 12.
  4. Write Sum as Exponent: Write the sum of the exponents as a single exponent. 12/4=312 / 4 = 3.
  5. Apply Sum to Base: Apply the sum of the exponents to the base rr. r12/4=r3r^{12/4} = r^3.

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