Final answer:
To simplify the expression (6u⁵y⁶-9u²y) ÷ (3u⁴y³), divide the coefficients and subtract the exponents of the variables. The simplified expression is 2uy³ - 3u^(-2)y^(-2).
Step-by-step explanation:
To simplify the expression (6u⁵y⁶-9u²y) ÷ (3u⁴y³), we divide the coefficients and then subtract the exponents of the variables. Dividing 6u⁵y⁶ by 3u⁴y³ gives us 2u^(5-4)y^(6-3), which simplifies to 2uy³. Dividing -9u²y by 3u⁴y³ gives us -3u^(2-4)y^(1-3), which simplifies to -3u^(-2)y^(-2). Therefore, the simplified expression is 2uy³ - 3u^(-2)y^(-2).
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