To find the product of [tex]\((-5xy^2)\)[/tex] and [tex]\((-4x^2y)\)[/tex], follow these steps:
1. Identify the coefficients: The coefficients of the given expressions are -5 and -4, respectively.
- Multiply these coefficients together:
[tex]\[
(-5) \times (-4) = 20
\][/tex]
Therefore, the coefficient of the product is 20.
2. Identify the exponents of [tex]\(x\)[/tex]:
- In the first expression, the exponent of [tex]\(x\)[/tex] is 1.
- In the second expression, the exponent of [tex]\(x\)[/tex] is 2.
- Add these exponents together:
[tex]\[
1 + 2 = 3
\][/tex]
Therefore, the exponent of [tex]\(x\)[/tex] in the product is 3.
3. Identify the exponents of [tex]\(y\)[/tex]:
- In the first expression, the exponent of [tex]\(y\)[/tex] is 2.
- In the second expression, the exponent of [tex]\(y\)[/tex] is 1.
- Add these exponents together:
[tex]\[
2 + 1 = 3
\][/tex]
Therefore, the exponent of [tex]\(y\)[/tex] in the product is 3.
So, the final product and the correct answers are:
- The coefficient of the product is 20.
- The exponent of [tex]\(x\)[/tex] in the product is 3.
- The exponent of [tex]\(y\)[/tex] in the product is 3.
