To simplify the given expression [tex]\(\left(3 x y^2\right)(4 x y)(2 x y)^3\)[/tex], we will proceed step-by-step.
1. First, simplify the exponentiation:
[tex]\[
(2 x y)^3 = (2)^3 \cdot (x)^3 \cdot (y)^3 = 8 x^3 y^3
\][/tex]
So, the expression [tex]\((2 x y)^3\)[/tex] simplifies to [tex]\(8 x^3 y^3\)[/tex].
2. Now, combine all the terms:
[tex]\[
(3 x y^2)(4 x y)(8 x^3 y^3)
\][/tex]
3. Calculate the product of the coefficients:
[tex]\[
3 \cdot 4 \cdot 8 = 96
\][/tex]
4. Combine the powers of [tex]\(x\)[/tex]:
[tex]\[
x^1 \cdot x^1 \cdot x^3 = x^{1+1+3} = x^5
\][/tex]
5. Combine the powers of [tex]\(y\)[/tex]:
[tex]\[
y^2 \cdot y^1 \cdot y^3 = y^{2+1+3} = y^6
\][/tex]
6. Put it all together:
[tex]\[
96 x^5 y^6
\][/tex]
Thus, the simplified form of the given expression [tex]\(\left(3 x y^2\right)(4 x y)(2 x y)^3\)[/tex] is [tex]\(\boxed{96 x^5 y^6}\)[/tex].
