Simplify. Assume all variables are positive. z^(3/4)/(z^(9/4) * z^(3/4)) 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^(3/4)/(z^(9/4) * z^(3/4))   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 Given Expression: Identify the given expression and the operation to be performed. The expression is z^(3/4) divided by (z^(9/4) * z^(3/4)). We need to simplify this expression using the properties of exponents.Apply Exponent Property for Multiplication: Apply the property of exponents for multiplication within the denominator. According to the property a^m * a^n = a^(m+n), we can add the exponents when multiplying like bases. So, z^(9/4) * z^(3/4) = z^(9/4 + 3/4).Calculate Exponent Sum: Calculate the sum of the exponents in the denominator. 9/4 + 3/4 = 12/4. So, z^(9/4) * z^(3/4) = z^(12/4).Simplify Denominator: Simplify the exponent in the denominator. 12/4 simplifies to 3. So, z^(9/4) * z^(3/4) = z^3.Rewrite Expression: Rewrite the original expression with the simplified denominator. The expression now is z^(3/4) / z^3.Apply Exponent Property for Division: Apply the property of exponents for division. According to the property a^m / a^n = a^(m-n), we can subtract the exponents when dividing like bases. So, z^(3/4) / z^3 = z^(3/4 - 3).Calculate Exponent Difference: Calculate the difference of the exponents. 3/4 - 3 is the same as 3/4 - 12/4, which equals -9/4. So, z^(3/4) / z^3 = z^(-9/4).Rewrite with Positive Exponent: Since we want all exponents to be positive, rewrite the expression with a positive exponent. According to the property a^(-n) = 1/a^n, we can write z^(-9/4) as 1/z^(9/4). So, z^(3/4) / z^3 = 1/z^(9/4).Check Final Expression: Check if the final expression answers the question prompt. The final expression is 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 the answer are positive.

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