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Simplify. Assume all variables are positive.\newliner114×r34r^{\frac{11}{4}} \times r^{\frac{3}{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.\newliner114×r34r^{\frac{11}{4}} \times r^{\frac{3}{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}.\newliner114×r34=r(114+34)r^{\frac{11}{4}} \times r^{\frac{3}{4}} = r^{\left(\frac{11}{4} + \frac{3}{4}\right)}.
  2. Perform Exponent Addition: Perform the addition of the exponents. (114)+(34)=144(\frac{11}{4}) + (\frac{3}{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}.\newliner144=r72r^{\frac{14}{4}} = r^{\frac{7}{2}}.
  4. Write Final Answer: Write the final 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.\newlineThe final answer is r72r^{\frac{7}{2}}.

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