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Simplify. Assume all variables are positive.\newlined25d135d^{\frac{2}{5}} \cdot d^{\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.\newlined25d135d^{\frac{2}{5}} \cdot d^{\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 Equation: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: \newlineam×an=a(m+n)a^m \times a^n = a^{(m+n)}\newlineSo, d25×d135=d25+135d^{\frac{2}{5}} \times d^{\frac{13}{5}} = d^{\frac{2}{5} + \frac{13}{5}}
  2. Add Exponents: Add the exponents.\newline25+135=(2+13)5\frac{2}{5} + \frac{13}{5} = \frac{(2 + 13)}{5}\newline25+135=155\frac{2}{5} + \frac{13}{5} = \frac{15}{5}
  3. Simplify Fraction: Simplify the fraction 155\frac{15}{5}.\newline155=3\frac{15}{5} = 3
  4. Write Final Answer: Write the final answer using the simplified exponent. d25×d135=d3d^{\frac{2}{5}} \times d^{\frac{13}{5}} = d^3

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