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Simplify. Assume all variables are positive.\newliner127×r97r^{\frac{12}{7}} \times 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______

Full solution

Q. Simplify. Assume all variables are positive.\newliner127×r97r^{\frac{12}{7}} \times 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: Identify the equation and apply the product of powers property.\newlineThe product of powers property states that when multiplying like bases, you add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlineSo, r127×r97=r127+97r^{\frac{12}{7}} \times r^{\frac{9}{7}} = r^{\frac{12}{7} + \frac{9}{7}}.
  2. Apply Product of Powers Property: Add the exponents.\newline127+97=(12+9)7=217\frac{12}{7} + \frac{9}{7} = \frac{(12 + 9)}{7} = \frac{21}{7}.
  3. Add Exponents: Simplify the exponent. 217\frac{21}{7} is equal to 33, so r217=r3r^{\frac{21}{7}} = r^3.
  4. Simplify Exponent: Write the final answer.\newlineThe simplified form of r12/7×r9/7r^{12/7} \times r^{9/7} is r3r^3.

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