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Simplify. Assume all variables are positive.\newliney32⋅y32y^{\frac{3}{2}} \cdot y^{\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______

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Full solution

Q. Simplify. Assume all variables are positive.\newliney32⋅y32y^{\frac{3}{2}} \cdot y^{\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 and apply 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=am+na^m \times a^n = a^{m+n}. y32×y32=y32+32y^{\frac{3}{2}} \times y^{\frac{3}{2}} = y^{\frac{3}{2} + \frac{3}{2}}
  2. Perform exponent addition: Perform the addition of the exponents. 32+32=62\frac{3}{2} + \frac{3}{2} = \frac{6}{2}
  3. Simplify fraction for new exponent: Simplify the fraction 62\frac{6}{2} to get the new exponent for yy.62=3\frac{6}{2} = 3
  4. Write final simplified expression: Write the final simplified expression using the new exponent. y32+32=y3y^{\frac{3}{2} + \frac{3}{2}} = y^3

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