To simplify the expression [tex]\(\left(2 x^3 y\right)\left(3 x^4 y^2\right)\)[/tex], we need to perform the multiplication step-by-step:
1. Multiply the coefficients:
[tex]\[
2 \cdot 3 = 6
\][/tex]
The combined coefficient is [tex]\(6\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]:
[tex]\[
x^3 \cdot x^4 = x^{3+4} = x^7
\][/tex]
When multiplying like bases, add the exponents.
3. Multiply the powers of [tex]\(y\)[/tex]:
[tex]\[
y \cdot y^2 = y^{1+2} = y^3
\][/tex]
Similarly, when multiplying like bases, add the exponents.
Putting it all together, the simplified expression is:
[tex]\[
6 x^7 y^3
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6x^7 y^3}
\][/tex]
