To simplify the expression [tex]\((4xy)(2x^2y)(3xy)^3\)[/tex], follow these steps:
1. Expand [tex]\((3xy)^3\)[/tex]:
[tex]\[
(3xy)^3 = 3^3 \cdot x^3 \cdot y^3 = 27x^3y^3
\][/tex]
2. Combine the expressions:
[tex]\[
(4xy)(2x^2y)(27x^3y^3)
\][/tex]
3. Multiply the coefficients:
[tex]\[
4 \cdot 2 \cdot 27 = 216
\][/tex]
4. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
x \cdot x^2 \cdot x^3 = x^{1+2+3} = x^6
\][/tex]
5. Combine the [tex]\(y\)[/tex] terms:
[tex]\[
y \cdot y \cdot y^3 = y^{1+1+3} = y^5
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
216 x^6 y^5
\][/tex]
Thus, the correct choice is:
[tex]\[
\boxed{216 x^6 y^5}
\][/tex]
