Simplify. Assume all variables are positive. u^(3/2)/(u^(3/2) * u^(1/2)) Write your answer in the form A or A/B, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. ______

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Simplify.  Assume all variables are positive. u^(3/2)/(u^(3/2) * u^(1/2))   Write your answer in the form A or A/B, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. ______

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Identify and apply quotient rule: Identify the expression and apply the quotient rule for exponents. The expression is u^(3/2)/(u^(3/2) * u^(1/2)). According to the quotient rule, when we divide like bases, we subtract the exponents: a^m / a^n = a^(m-n).Apply product rule to denominator: Apply the product rule for exponents to the denominator. The product rule states that when we multiply like bases, we add the exponents: a^m * a^n = a^(m+n). So, u^(3/2) * u^(1/2) = u^(3/2 + 1/2).Perform exponent addition: Perform the addition in the exponent. Add the exponents in the denominator: 3/2 + 1/2 = 4/2 = 2. So, u^(3/2) * u^(1/2) = u^2.Apply quotient rule to original expression: Apply the quotient rule to the original expression. Now we have u^(3/2) / u^2. Using the quotient rule: u^(3/2 - 2) = u^(3/2 - 4/2).Perform exponent subtraction: Perform the subtraction in the exponent. Subtract the exponents: 3/2 - 4/2 = -1/2. So, u^(3/2) / u^2 = u^(-1/2).Write final answer: Write the final answer with a positive exponent. Since we want the exponent to be positive, we can write u^(-1/2) as 1/u^(1/2).

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