Warm Up
Lin and Diego are discussing two expressions: and .
Lin says, “I think the two expressions are equivalent.”
Diego says, “I think the two expressions are only equal for some values of .”
Do you agree with either of them? Explain or show your reasoning.
Your answer may vary, but here is a sample:
I agree with Diego. Sample explanation: If we find the value of and for different values of , say 0, 1, 2, 3, and 4, we can see that they are not always equal. As the table shows, they are only equal sometimes, for example, when is 2 and 4.
1 | 1 | 2 |
2 | 4 | 4 |
3 | 9 | 8 |
4 | 16 | 16 |
5 | 25 | 32 |
10 | 100 | 1,024 |