Final answer:
The simplified expression after multiplying 3x^5 * 4y * 3y^8 * x^4 is 36x^9y^9.
Step-by-step explanation:
To multiply the given terms 3x5 * 4y * 3y8 * x4 and simplify the expression, we need to combine like terms by adding the exponents of like bases and multiply the coefficients.
Step 1: Multiply the coefficients (numbers in front of the variables): 3 * 4 * 3 = 36.
Step 2: Combine the like variables by adding their exponents. For x, we have x5 and x4, which means we add their exponents: 5 + 4 = 9, resulting in x9.
Step 3: For y, we have just y (which is y1) and y8, which gives us 1 + 8 = 9, resulting in y9.
Therefore, the simplified expression is 36x9y9.