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Simplify. Assume all variables are positive.\newlined74d14d^{\frac{7}{4}} \cdot d^{\frac{1}{4}}\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.\newlined74d14d^{\frac{7}{4}} \cdot d^{\frac{1}{4}}\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×dcd=d(ab+cd)d^{\frac{a}{b}} \times d^{\frac{c}{d}} = d^{\left(\frac{a}{b} + \frac{c}{d}\right)}.
  2. Add Exponents: Add the exponents 74\frac{7}{4} and 14\frac{1}{4}: (74)+(14)=84\left(\frac{7}{4}\right) + \left(\frac{1}{4}\right) = \frac{8}{4}.
  3. Simplify Fraction: Simplify the fraction 84\frac{8}{4} to its lowest terms, which is 22.
  4. Write Final Answer: Write the final answer using the simplified exponent: d2d^2.

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