Simplify. Assume all variables are positive. r^(3/2) * r^(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. r^(3/2) * r^(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 Equation and Apply Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: a^m * a^n = a^(m+n). So, r^(3/2) * r^(5/2) = r^(3/2 + 5/2).Add Exponents: Add the exponents: 3/2 + 5/2. This is a simple fraction addition where the denominators are the same, so we add the numerators: 3 + 5 = 8. Therefore, r^(3/2 + 5/2) = r^(8/2).Simplify Exponent: Simplify the exponent: 8/2. Divide 8 by 2 to get 4. So, r^(8/2) = r^4.Check Final Exponent: Check that the final exponent is positive and that there are no variables in common in the numerator and denominator, as per the instructions. Since r^4 is already in its simplest form with a positive exponent and no denominator, we have completed the problem.

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