Answer: The value of ab^3, in fully simplified form, is 8ix - 16.
Step-by-step explanation: We enter the known values of a and b into the following formula to get the value of ab3:
a = -x + 2i b = 2i
ab^3 = (-x + 2i)(2i)^3
Let's first simplify (2i)3:
(2i)^3 = 2^3 * i^3 = 8 * (-i) = -8i
We now re-enter this value into the expression:
ab^3 = (-x + 2i)(-8i)
We employ the distributive property to further simplify this:
-8i(-x) + (-8i)(2i) = ab3
Increasing the terms by
ab^3 = 8ix + 16i^2
Since the definition of i2 is -1, we can further simplify:
ab^3 = 8ix + 16(-1)
ab^3 = 8ix - 16
As a result, ab3 has the value 8ix - 16 in fully simplified form.