Simplify. Assume all variables are positive. d^(3/4)/(d^(5/4) * d^(9/4)) 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. d^(3/4)/(d^(5/4) * d^(9/4))   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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Combine Exponents in Denominator: Combine the exponents in the denominator using the property of exponents that states when you multiply like bases, you add the exponents. d^(5/4) * d^(9/4) = d^(5/4 + 9/4)Add Exponents in Denominator: Add the exponents in the denominator. 5/4 + 9/4 = 14/4 So, d^(5/4) * d^(9/4) = d^(14/4)Simplify Exponent in Denominator: Simplify the exponent in the denominator. 14/4 = 3.5 or 7/2 So, d^(5/4) * d^(9/4) = d^(7/2)Divide Exponents: Divide the exponents using the property of exponents that states when you divide like bases, you subtract the exponents. d^(3/4) / d^(7/2)Convert Exponents to Common Denominator: Convert the exponents to have a common denominator before subtracting. 3/4 is the same as 6/8 and 7/2 is the same as 28/8. So, d^(3/4) / d^(7/2) = d^(6/8) / d^(28/8)Subtract Exponents: Subtract the exponents in the numerator and the denominator. 6/8 - 28/8 = -22/8 So, d^(3/4) / d^(7/2) = d^(-22/8)Simplify Negative Exponent: Simplify the negative exponent by writing it as a positive exponent in the denominator. d^(-22/8) = 1 / d^(22/8)Simplify Exponent in Denominator: Simplify the exponent in the denominator. 22/8 can be reduced to 11/4. So, 1 / d^(22/8) = 1 / d^(11/4)

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