To find the product \(a^3b^2 \cdot 4ab^3\), we multiply the coefficients and add the exponents of each variable:
For \(a\): \(a^3 \cdot a^1 = a^{3+1} = a^4\)
For \(b\): \(b^2 \cdot b^3 = b^{2+3} = b^5\)
So, the product is \(4a^4b^5\).
Therefore, the correct option is B. \(4a^4b^5\).
