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Simplify. Assume all variables are positive.\newlinex52×x12x^{\frac{5}{2}} \times x^{\frac{1}{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.\newlinex52×x12x^{\frac{5}{2}} \times x^{\frac{1}{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 expression: Identify the expression to be simplified.\newlineWe have the expression x5/2×x1/2x^{5/2} \times x^{1/2} and we need to simplify it.
  2. Apply product rule: Apply the product rule for exponents.\newlineThe product rule states that when multiplying two powers with the same base, you add the exponents. So, we add the exponents 52\frac{5}{2} and 12\frac{1}{2}.\newlinex52x12=x52+12x^{\frac{5}{2}} * x^{\frac{1}{2}} = x^{\frac{5}{2} + \frac{1}{2}}
  3. Perform addition: Perform the addition of the exponents. 52+12=62\frac{5}{2} + \frac{1}{2} = \frac{6}{2}
  4. Simplify exponent: Simplify the exponent. 62=3\frac{6}{2} = 3
  5. Write final expression: Write the final simplified expression. x52×x12=x3x^{\frac{5}{2}} \times x^{\frac{1}{2}} = x^3

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