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Simplify. Assume all variables are positive.\newlinex12×x32x^{\frac{1}{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.\newlinex12×x32x^{\frac{1}{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: Identify the equation and apply the property of exponents for multiplication, which states that when you multiply 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 12\frac{1}{2} and 32\frac{3}{2}.$12+32=42\$\frac{1}{2} + \frac{3}{2} = \frac{4}{2}\)
  3. Simplify Fraction: Simplify the fraction 42\frac{4}{2} to get 22.\newline42=2\frac{4}{2} = 2
  4. Write Final Expression: Write the final simplified expression using the sum of the exponents. x12+32=x2x^{\frac{1}{2} + \frac{3}{2}} = x^2

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