Simplify. Assume all variables are positive. x^(2/3)/(x^(5/3) * x^(1/3)) 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^(2/3)/(x^(5/3) * x^(1/3))   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: Combine the exponents in the denominator using the property of exponents that states when you multiply like bases, you add the exponents. x^(5/3) * x^(1/3) = x^(5/3 + 1/3)Add Exponents: Add the exponents in the denominator. 5/3 + 1/3 = 6/3 x^(5/3 + 1/3) = x^(6/3)Simplify Exponent: Simplify the exponent in the denominator. 6/3 = 2 x^(6/3) = x^2Rewrite Expression: Rewrite the original expression with the simplified denominator. x^(2/3) / (x^(5/3) * x^(1/3)) = x^(2/3) / x^2Apply Property: Apply the property of exponents that states when you divide like bases, you subtract the exponents. x^(2/3) / x^2 = x^(2/3 - 2)Convert Exponent: Convert the whole number exponent to a fraction to subtract the exponents. 2 = 6/3 x^(2/3 - 2) = x^(2/3 - 6/3)Subtract Exponents: Subtract the exponents. 2/3 - 6/3 = -4/3 x^(2/3 - 6/3) = x^(-4/3)Rewrite Exponent: Since we want all exponents to be positive, we can rewrite x^(-4/3) as 1/x^(4/3). x^(-4/3) = 1/x^(4/3)

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