Final answer:
Divide each term of the polynomial by -3u⁵x⁴ separately, dividing the coefficients and subtracting the exponents for corresponding variables u and x. Simplify each term to obtain the final simplified expression.
Step-by-step explanation:
To divide the given algebraic expression by -3u⁵x⁴, you divide each term of the expression separately. Start with the first term 24u²x³, and divide this by -3u⁵x⁴. To do this, divide the coefficients (24 divided by -3) and subtract the exponents of corresponding variables (u and x). This process is repeated for each term in the polynomial expression. Dividing the first term gives you -8u-3x-1. Apply the same logic to the remaining terms: -27u⁶x⁷ divided by -3u⁵x⁴ gives you 9ux³, and 20u⁵x⁴ divided by -3u⁵x⁴ gives you -20/3. After completion, ensure to simplify each term if possible.