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Simplify. Assume all variables are positive.\newlined52d32d^{\frac{5}{2}} \cdot d^{\frac{3}{2}}\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.\newlined52d32d^{\frac{5}{2}} \cdot d^{\frac{3}{2}}\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 and Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: am×an=a(m+n)a^m \times a^n = a^{(m+n)}. So, d(5/2)×d(3/2)=d((5/2)+(3/2))d^{(5/2)} \times d^{(3/2)} = d^{((5/2) + (3/2))}.
  2. Add Exponents: Perform the addition of the exponents: (52)+(32)=82(\frac{5}{2}) + (\frac{3}{2}) = \frac{8}{2}.
  3. Simplify Fraction: Simplify the fraction 82\frac{8}{2} to get 44.
  4. Write Final Answer: Write the final answer using the simplified exponent: d4d^4.

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