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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 Equation Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: dab×dcb=d(a+c)bd^{\frac{a}{b}} \times d^{\frac{c}{b}} = d^{\frac{(a+c)}{b}}.
  2. Add Exponents of dd: Add the exponents of dd: (97)+(137)\left(\frac{9}{7}\right) + \left(\frac{13}{7}\right).
  3. Calculate Sum: Calculate the sum of the exponents: (97)+(137)=9+137=227(\frac{9}{7}) + (\frac{13}{7}) = \frac{9+13}{7} = \frac{22}{7}.
  4. Write Final Expression: Write the final simplified expression using the sum of the exponents: d227d^{\frac{22}{7}}.

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