Final answer:
The expression (32y⁵z-13y⁵z⁵-20y⁷z⁷) divided by (-4y⁴z³) simplifies to -8y - ¼yz² + 5y³z⁴ by dividing each term in the numerator by the denominator and simplifying each resulting term.
Step-by-step explanation:
To simplify the expression (32y⁵z-13y⁵z⁵-20y⁷z⁷) divided by (-4y⁴z³), we perform polynomial division by dividing each term in the numerator by the denominator:
- 32y⁵z ÷ -4y⁴z³ = -8y (because y⁵ ÷ y⁴ = y and z ÷ z³ = z⁻²)
- -13y⁵z⁵ ÷ -4y⁴z³ = 3¼ yz² (because y⁵ ÷ y⁴ = y and z⁵ ÷ z³ = z²)
- -20y⁷z⁷ ÷ -4y⁴z³ = 5y³z⁴ (because y⁷ ÷ y⁴ = y³ and z⁷ ÷ z³ = z⁴)
Combining these terms, the simplified result is: -8y - ½yz² + 5y³z⁴.