Final answer:
Divide the coefficients and subtract the exponents of the variables. The simplified answer is -5z^1u^2 + 1.5z^1u^(-1).
Step-by-step explanation:
To divide the expressions (10z⁵u⁴-3z⁵u) and (-2z⁴u²), we can divide the coefficients and subtract the exponents of the variables. In this case, dividing (10z⁵u⁴-3z⁵u) by (-2z⁴u²) gives us:
(10/-2)z^(5-4)u^(4-2) - (3/-2)z^(5-4)u^(1-2)
Simplifying further, we get:
-5z^(1)u^(2) + 1.5z^(1)u^(-1)
Therefore, the simplified answer is -5z^1u^2 + 1.5z^1u^(-1).