Final answer:
The expression "i ⁸²" appears to be a typo, but it seems to involve simplifying powers of the imaginary unit i. If interpreted as i to the power of 82, the pattern of powers of i repeats every four terms. However, the correct simplification of i² is -1.
Step-by-step explanation:
The question "i ⁸²" seems to relate to the mathematical concept of imaginary numbers, where i is the imaginary unit defined as the square root of -1. However, there seems to be a typo or confusion in this expression. In mathematics, powers of i follow a specific pattern: i, i², i³, i⁴, and so on, where i² equals -1, i³ equals -i, i⁴ equals 1, and this pattern repeats every four powers. Thus, to simplify i ⁸², one would break down the exponent 82 into multiples of 4 to determine the corresponding power of i. It's likely that the correct expression was intended to be i², which simply simplifies to -1.