To simplify the expression [tex]\(\left(-3 x^2 y\right)\left(2 x y^3\right)\)[/tex], follow these steps:
1. Multiply the constants:
- We have -3 and 2.
- [tex]\(-3 \cdot 2 = -6\)[/tex].
2. Multiply the [tex]\(x\)[/tex] terms:
- [tex]\(x^2\)[/tex] from the first expression and [tex]\(x\)[/tex] from the second.
- When multiplying the same base with exponents, add the exponents: [tex]\(x^2 \cdot x = x^{2+1} = x^3\)[/tex].
3. Multiply the [tex]\(y\)[/tex] terms:
- [tex]\(y\)[/tex] from the first expression and [tex]\(y^3\)[/tex] from the second.
- Again, add the exponents: [tex]\(y \cdot y^3 = y^{1+3} = y^4\)[/tex].
4. Combine all parts:
- The constant part is [tex]\(-6\)[/tex].
- The [tex]\(x\)[/tex] part is [tex]\(x^3\)[/tex].
- The [tex]\(y\)[/tex] part is [tex]\(y^4\)[/tex].
- Putting it all together, we get [tex]\(-6 x^3 y^4\)[/tex].
Thus, the simplified expression is:
[tex]\[ \boxed{-6 x^3 y^4} \][/tex]
