Simplify. Assume all variables are positive. z^(1/2)/(z^(3/2) * z^(3/2)) 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. z^(1/2)/(z^(3/2) * z^(3/2))   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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Given Expression: We are given the expression z^(1/2)/(z^(3/2) * z^(3/2)). To simplify this expression, we will use the properties of exponents to combine the exponents in the denominator and then simplify the fraction.Combine Exponents in Denominator: First, let's combine the exponents in the denominator using the property of exponents that states a^(m) * a^(n) = a^(m+n). We have z^(3/2) * z^(3/2) which equals z^(3/2 + 3/2).Simplify Denominator: Adding the exponents in the denominator, we get z^(3/2 + 3/2) = z^(6/2). Simplifying 6/2 gives us z^3.Combine Exponents in Numerator: Now we have the expression z^(1/2) / z^3. To simplify this, we use the property of exponents that states a^(m) / a^(n) = a^(m-n) when m > n. Here, we have z^(1/2 - 3).Simplify Numerator: Subtracting the exponents, we get z^(1/2 - 3) = z^(1/2 - 6/2) = z^(-5/2). Since we want the exponent to be positive, we can write this as 1/z^(5/2).Final Simplification: The expression is now simplified to 1/z^(5/2), which is in the form A/B as required, where A is 1 and B is z^(5/2). There are no variables in common in the numerator and denominator, and the exponent is positive.

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