Final answer:
To simplify the expression (12z⁶u⁵+27z²u-25z⁴u²)-:(-3z⁴u²), divide each term inside the parentheses by -3z⁴u² and simplify to get -36z⁶u³ - 81z²u³ + 75.
Step-by-step explanation:
To simplify the expression (12z⁶u⁵+27z²u-25z⁴u²)-:(-3z⁴u²), we need to divide each term inside the parentheses by -3z⁴u². This is equivalent to multiplying each term by the reciprocal of -3z⁴u², which is 1/(-3z⁴u²).
Using the laws of exponents and simplifying, we get:
(12z⁶u⁵)/(1/(-3z⁴u²)) + (27z²u)/(1/(-3z⁴u²)) - (25z⁴u²)/(1/(-3z⁴u²))
which simplifies to:
(-36z⁶u³) + (-81z²u³) + (75)
Therefore, the simplified expression is -36z⁶u³ - 81z²u³ + 75.