Simplify. Assume all variables are positive. x^(2/3)/x^(8/3) 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^(8/3)   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

Identify expression: Identify the expression to simplify. We have the expression x^(2/3)/x^(8/3) and we need to simplify it.Apply quotient rule: Apply the quotient rule for exponents. The quotient rule states that when we divide two exponents with the same base, we subtract the exponents: a^m / a^n = a^(m-n). So, x^(2/3)/x^(8/3) = x^((2/3)-(8/3)).Perform subtraction: Perform the subtraction of the exponents. (2/3) - (8/3) = -6/3.Simplify result: Simplify the result of the subtraction. -6/3 simplifies to -2.Write simplified exponent: Write the simplified exponent with the base x. x^((2/3)-(8/3)) = x^(-2).Use property: Since we want all exponents to be positive, we use the property that x^(-a) = 1/x^a. Therefore, x^(-2) = 1/x^2.

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