Final answer:
To evaluate (4^3)^1, raise 4 to the power of 3, which is 64, and then raise 64 to the power of 1, resulting in 64. The classmate likely made an error by not raising the result to the power of 1.
Step-by-step explanation:
To evaluate the expression (4^3)^1, we need to raise 4 to the power of 3 first, which gives us 4 * 4 * 4 = 64. Now, we raise 64 to the power of 1, which is just 64. Therefore, the expression evaluates to 64.
The likely error in your classmate's answer of 256 is that they mistakenly raised 4 to the power of 3, but then stopped and did not raise the result to the power of 1. So their answer is incorrect.