Simplify. Assume all variables are positive. x^(1/4)/(x^(3/4) * x^(7/4)) 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. x^(1/4)/(x^(3/4) * x^(7/4))   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. x^(3/4) * x^(7/4) = x^(3/4 + 7/4)Add exponents in denominator: Add the exponents in the denominator. 3/4 + 7/4 = 10/4 So, x^(3/4) * x^(7/4) = x^(10/4)Simplify exponent in denominator: Simplify the exponent in the denominator. 10/4 can be simplified to 5/2. So, x^(3/4) * x^(7/4) = x^(5/2)Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. x^(1/4) / (x^(3/4) * x^(7/4)) = x^(1/4) / x^(5/2)Subtract exponents to divide: Subtract the exponents to divide the expressions with the same base using the property of exponents that states when you divide like bases, you subtract the exponents. x^(1/4) / x^(5/2) = x^(1/4 - 5/2)Convert exponents to common denominator: Convert the exponents to have a common denominator before subtracting. 5/2 is the same as 10/4, so we have: x^(1/4 - 10/4)Subtract exponents: Subtract the exponents. 1/4 - 10/4 = -9/4 So, x^(1/4) / x^(5/2) = x^(-9/4)Rewrite as positive exponent: Since we want the exponent to be positive, we can rewrite x^(-9/4) as 1 / x^(9/4).

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