Final answer:
The last two digits of (4362)⁴⁸² are 44.
Step-by-step explanation:
To evaluate the last two digits of the number (4362) raised to the exponent 482, we can use the concept of cyclicity of the last two digits of powers.
The last two digits of 4362 follow a cyclical pattern: 62, 44, 28, 96, 32, 04. Since the exponent 482 is divisible by 6 (the length of the cycle), the last two digits of (4362)⁴⁸² will be the same as the last two digits of (4362)², which is 44.
Therefore, the last two digits of (4362)⁴⁸² are 44.