Simplify. Assume all variables are positive. b^(3/2)/b^(5/2) 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. ______

Question

Simplify.  Assume all variables are positive. b^(3/2)/b^(5/2)   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 b^(3/2) / b^(5/2). We need to simplify this expression using the properties of exponents.Apply Quotient Rule: Apply the quotient rule for exponents. The quotient rule states that when dividing like bases with exponents, we subtract the exponents: a^m / a^n = a^(m-n). So, b^(3/2) / b^(5/2) = b^(3/2 - 5/2).Perform Subtraction: Perform the subtraction of the exponents. Subtract the exponents: 3/2 - 5/2 = -2/2.Simplify Result: Simplify the result. Since -2/2 is equal to -1, we have b^(-1).Write Final Answer: Write the final answer with a positive exponent. To express b^(-1) with a positive exponent, we take the reciprocal of b, which is 1/b.

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