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Simplify. Assume all variables are positive.\newlinet65t115t^{\frac{6}{5}} \cdot t^{\frac{11}{5}}\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.\newlinet65t115t^{\frac{6}{5}} \cdot t^{\frac{11}{5}}\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 Exponent Rule: Identify the equation and apply the exponent multiplication rule.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinet65×t115=t65+115t^{\frac{6}{5}} \times t^{\frac{11}{5}} = t^{\frac{6}{5} + \frac{11}{5}}
  2. Add Exponents: Add the exponents.\newline65+115=(6+11)5\frac{6}{5} + \frac{11}{5} = \frac{(6 + 11)}{5}\newline65+115=175\frac{6}{5} + \frac{11}{5} = \frac{17}{5}
  3. Write Final Answer: Write the final answer with the combined exponent. t65×t115=t175t^{\frac{6}{5}} \times t^{\frac{11}{5}} = t^{\frac{17}{5}}

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