To simplify the expression [tex]\(\left(4 x^3 y^3\right)\left(2 x^2 y\right)\)[/tex], follow these steps:
1. Distribute the constants:
First, multiply the numerical coefficients (constants) together:
[tex]\[ 4 \times 2 = 8 \][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
Multiply the [tex]\(x\)[/tex] terms by adding their exponents (because they have the same base, [tex]\(x\)[/tex]):
[tex]\[ x^3 \times x^2 = x^{3+2} = x^5 \][/tex]
3. Combine the [tex]\(y\)[/tex] terms:
Multiply the [tex]\(y\)[/tex] terms by adding their exponents (because they have the same base, [tex]\(y\)[/tex]):
[tex]\[ y^3 \times y = y^{3+1} = y^4 \][/tex]
Putting it all together, the simplified expression is:
[tex]\[ 8 x^5 y^4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{8 x^5 y^4} \][/tex]
