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Simplify. Assume all variables are positive.\newlined97d137d^{\frac{9}{7}} \cdot d^{\frac{13}{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.\newlined97d137d^{\frac{9}{7}} \cdot d^{\frac{13}{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 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: am×an=am+na^m \times a^n = a^{m+n}.\newlined97×d137=d97+137d^{\frac{9}{7}} \times d^{\frac{13}{7}} = d^{\frac{9}{7} + \frac{13}{7}}.
  2. Add Exponents: Add the exponents.\newline97+137=(9+13)7\frac{9}{7} + \frac{13}{7} = \frac{(9 + 13)}{7}.
  3. Perform Addition: Perform the addition.\newline(9+13)/7=22/7(9 + 13) / 7 = 22/7.
  4. Write Final Answer: Write the final answer using the simplified exponent. d97×d137=d227d^{\frac{9}{7}} \times d^{\frac{13}{7}} = d^{\frac{22}{7}}.

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