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Simplify. Assume all variables are positive.\newlinet25t75t^{\frac{2}{5}} \cdot t^{\frac{7}{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.\newlinet25t75t^{\frac{2}{5}} \cdot t^{\frac{7}{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 Equation & Apply Property: Identify the equation and apply the product of powers property.\newlineThe product of powers property states that when you multiply two exponents with the same base, you add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinet25×t75=t25+75t^{\frac{2}{5}} \times t^{\frac{7}{5}} = t^{\frac{2}{5} + \frac{7}{5}}
  2. Add Exponents: Add the exponents.\newlineSince the base tt is the same, we add the exponents 25\frac{2}{5} and 75\frac{7}{5}.\newline25+75=95\frac{2}{5} + \frac{7}{5} = \frac{9}{5}
  3. Write Final Answer: Write the final answer with the combined exponent. t25×t75=t95t^{\frac{2}{5}} \times t^{\frac{7}{5}} = t^{\frac{9}{5}}

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