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Simplify. Assume all variables are positive.\newlinev75v135v^{\frac{7}{5}} \cdot v^{\frac{13}{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.\newlinev75v135v^{\frac{7}{5}} \cdot v^{\frac{13}{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 Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: \newlinev75×v135=v75+135v^{\frac{7}{5}} \times v^{\frac{13}{5}} = v^{\frac{7}{5} + \frac{13}{5}}
  2. Add Exponents: Add the exponents.\newline75+135=(7+13)5=205\frac{7}{5} + \frac{13}{5} = \frac{(7 + 13)}{5} = \frac{20}{5}
  3. Simplify Fraction: Simplify the fraction 205\frac{20}{5}.\newline205=4\frac{20}{5} = 4
  4. Write Final Answer: Write the final answer using the simplified exponent. v75×v135=v4v^{\frac{7}{5}} \times v^{\frac{13}{5}} = v^4

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