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Simplify. Assume all variables are positive.\newliner127r97r^{\frac{12}{7}} \cdot r^{\frac{9}{7}}\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______

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Q. Simplify. Assume all variables are positive.\newliner127r97r^{\frac{12}{7}} \cdot r^{\frac{9}{7}}\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}.\newliner127×r97=r127+97r^{\frac{12}{7}} \times r^{\frac{9}{7}} = r^{\frac{12}{7} + \frac{9}{7}}.
  2. Add Exponents: Add the exponents. 127+97=(12+9)7=217.\frac{12}{7} + \frac{9}{7} = \frac{(12 + 9)}{7} = \frac{21}{7}.
  3. Apply Exponents to Base: Apply the sum of the exponents to the base rr.r127×r97=r217r^{\frac{12}{7}} \times r^{\frac{9}{7}} = r^{\frac{21}{7}}.
  4. Simplify Exponent: Simplify the exponent if possible.\newlineSince 21/721/7 is a division of two integers where the numerator is divisible by the denominator, we can simplify it to a whole number.\newline21/7=321/7 = 3.
  5. Write Final Answer: Write the final answer with a positive exponent. r217=r3r^{\frac{21}{7}} = r^3.

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