Simplify. Assume all variables are positive. b^(7/4)/(b^(3/4) * b^(7/4)) 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^(7/4)/(b^(3/4) * b^(7/4))   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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Identify Given Expression: Identify the given expression and the properties of exponents that will be used to simplify it. The expression is b^(7/4) / (b^(3/4) * b^(7/4)). We will use the properties of exponents, specifically the quotient rule (a^m / a^n = a^(m-n)) and the product rule (a^m * a^n = a^(m+n)).Apply Product Rule: Apply the product rule to the denominator of the expression. According to the product rule, when multiplying two exponents with the same base, you add the exponents: b^(3/4) * b^(7/4) = b^(3/4 + 7/4).Calculate Sum of Exponents: Calculate the sum of the exponents in the denominator. Adding the exponents: 3/4 + 7/4 = 10/4, which simplifies to 5/2. So, b^(3/4) * b^(7/4) = b^(5/2).Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. The expression now is b^(7/4) / b^(5/2).Apply Quotient Rule: Apply the quotient rule to simplify the expression. According to the quotient rule, when dividing two exponents with the same base, you subtract the exponents: b^(7/4) / b^(5/2) = b^(7/4 - 5/2).Convert Exponents: Convert the exponents to have a common denominator before subtracting. The common denominator for 4 and 2 is 4. Convert 5/2 to 10/4 so that both exponents have the same denominator: b^(7/4 - 10/4).Calculate Difference of Exponents: Calculate the difference of the exponents. Subtracting the exponents: 7/4 - 10/4 = -3/4. So, b^(7/4) / b^(5/2) = b^(-3/4).Rewrite as Reciprocal: Since negative exponents indicate the reciprocal, rewrite b^(-3/4) as 1/b^(3/4). The expression b^(-3/4) is equivalent to 1/b^(3/4) according to the negative exponent rule.

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