Simplify. Assume all variables are positive. b^(2/3)/b^(4/3) 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. b^(2/3)/b^(4/3)   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 Equation & Apply Quotient Rule: Identify the equation and apply the quotient rule for exponents. The quotient rule states that when dividing like bases with exponents, you subtract the exponents: a^m / a^n = a^(m-n). So, b^(2/3) / b^(4/3) = b^(2/3 - 4/3).Subtract Exponents: Subtract the exponents. 2/3 - 4/3 = -2/3. So, b^(2/3) / b^(4/3) = b^(-2/3).Rewrite Negative Exponent: Since we want all exponents to be positive, we can rewrite b^(-2/3) as 1/b^(2/3). This is because a negative exponent indicates the reciprocal of the base raised to the positive of that exponent.Check Final Answer: Check the final answer for any common variables in the numerator and denominator and ensure all exponents are positive. We have 1/b^(2/3), which has no variables in common between the numerator and denominator, and the exponent is positive.

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