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Simplify. Assume all variables are positive.\newlinex32×x32x^{\frac{3}{2}} \times x^{\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.\newlinex32×x32x^{\frac{3}{2}} \times x^{\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 Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: xa×xb=x(a+b)x^a \times x^b = x^{(a+b)}.
  2. Add Exponents: Add the exponents (32)+(32)(\frac{3}{2}) + (\frac{3}{2}).
  3. Calculate Sum: Calculate the sum of the exponents: (32)+(32)=62(\frac{3}{2}) + (\frac{3}{2}) = \frac{6}{2}.
  4. Simplify Fraction: Simplify the fraction 62\frac{6}{2} to get 33.
  5. Write Final Answer: Write the final answer using the simplified exponent: x3x^3.

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