Simplify. Assume all variables are positive. t^(3/2)/(t^(3/2) * t^(1/2)) 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. ______

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Simplify.  Assume all variables are positive. t^(3/2)/(t^(3/2) * t^(1/2))   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

Apply Exponent Properties: Write down the expression and apply the properties of exponents. We have the expression t^(3/2)/(t^(3/2) * t^(1/2)). According to the properties of exponents, when we multiply terms with the same base, we add their exponents. So, t^(3/2) * t^(1/2) becomes t^(3/2 + 1/2).Add Exponents of t: Add the exponents of t. t^(3/2 + 1/2) = t^(2/2) = t^1 = t. So, the expression in the denominator simplifies to t.Divide Terms with Same Base: Divide the terms with the same base. Now we have t^(3/2) / t. Since t = t^1, we can write this as t^(3/2) / t^1. According to the properties of exponents, when we divide terms with the same base, we subtract their exponents. So, t^(3/2) / t^1 becomes t^(3/2 - 1).Subtract Exponents of t: Subtract the exponents of t. t^(3/2 - 1) = t^(3/2 - 2/2) = t^(1/2). So, the expression simplifies to t^(1/2).Write Final Answer: Write the final answer. Since t^(1/2) is already in its simplest form and all exponents are positive, this is our final answer.

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