Simplify. Assume all variables are positive. x^(1/4)/(x^(3/4) * x^(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. x^(1/4)/(x^(3/4) * x^(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. ______

Bytelearn · Accepted Answer

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^(9/4) = x^(3/4 + 9/4)Add exponents in denominator: Add the exponents in the denominator. 3/4 + 9/4 = 12/4 x^(3/4) * x^(9/4) = x^(12/4)Simplify exponent in denominator: Simplify the exponent in the denominator. 12/4 = 3 x^(12/4) = x^3Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. x^(1/4) / (x^3)Apply property of exponents: Apply the property of exponents that states when you divide like bases, you subtract the exponents. x^(1/4) / x^3 = x^(1/4 - 3)Convert whole number exponent: Convert the whole number exponent to a fraction to have a common denominator. 3 = 12/4 x^(1/4 - 3) = x^(1/4 - 12/4)Subtract exponents: Subtract the exponents. 1/4 - 12/4 = -11/4 x^(1/4 - 12/4) = x^(-11/4)Rewrite with positive exponent: Since we want the exponent to be positive, we can rewrite the expression with a positive exponent by taking the reciprocal of the base. x^(-11/4) = 1/x^(11/4)

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