To simplify the expression [tex]\((4xy)(2x^2y)(3xy)^3\)[/tex], we follow these steps:
1. First, simplify the exponents within the terms.
2. Rewrite [tex]\((3xy)^3\)[/tex]:
[tex]\[
(3xy)^3 = 3^3 \cdot x^3 \cdot y^3 = 27x^3y^3
\][/tex]
Hence, the expression becomes:
[tex]\[
(4xy)(2x^2y)(27x^3y^3)
\][/tex]
3. Now, multiply all the coefficients together:
[tex]\[
4 \cdot 2 \cdot 27 = 216
\][/tex]
4. Next, combine the powers of [tex]\(x\)[/tex]:
[tex]\[
x \cdot x^2 \cdot x^3 = x^{1+2+3} = x^6
\][/tex]
5. Finally, combine the powers of [tex]\(y\)[/tex]:
[tex]\[
y \cdot y \cdot y^3 = y^{1+1+3} = y^5
\][/tex]
Putting it all together, we get:
[tex]\[
216x^6y^5
\][/tex]
Therefore, the simplified expression is [tex]\(216x^6y^5\)[/tex], and the correct answer is:
[tex]\[
\boxed{216x^6y^5}
\][/tex]
