Final answer:
The exact value of the expression 3∆(-2), where the operation m∆n is defined as 2m² - 3n³, is 42.
Step-by-step explanation:
If m∆n denotes the operation given by 2m² - 3n³, to determine the exact value of 3∆(-2), we plug in m = 3 and n = -2 into the expression.
So, we have: 3∆(-2) = 2(3)² - 3(-2)³ = 2×9 - 3×(-8) = 18 + 24 = 42.
Therefore, the exact value of 3∆(-2) is 42.