Final answer:
To divide (12y)/(b^4) by (4y^3)/(3b^5y), multiply by the reciprocal of the second expression, simplify the coefficients and the variables by subtracting exponents, cancel like terms to get the simplified answer 9b/y.
Step-by-step explanation:
To divide the given rational expressions, (12y)/(b^4) by (4y^3)/(3b^5y), we follow the division rule for exponential expressions. First, transform the division into multiplication by the reciprocal of the second expression. Then divide the coefficients (numeric parts) and subtract the exponents of the variables with the same base.
Step-by-step:
1. Write the problem as (12y)/(b^4) * (3b^5y)/(4y^3).
2. Multiply the coefficients: 12 * 3 = 36 and 4.
3. Combine the y terms by subtracting exponents: y^1 / y^3 = 1/y^2.
4. Combine the b terms by subtracting exponents: b^5 / b^4 = b^1.
5. Cancel and simplify: (36 * b * y) / (4 * y^2) simplifies to 9b/y.
The final simplified answer is 9b/y.