To determine which of these expressions is not a square, we’ll evaluate each one to see if it results in a perfect square (a number that is an integer squared).

1. $1^6 = 1$: $1$ is a perfect square, as $1 = 1^2$.
2. $2^5 = 32$: $32$ is not a perfect square (no integer squared gives $32$).
3. $3^4 = 81$: $81$ is a perfect square, as $81 = 9^2$.
4. $4^3 = 64$: $64$ is a perfect square, as $64 = 8^2$.
5. $5^2 = 25$: $25$ is a perfect square, as $25 = 5^2$.

Conclusion: $2^5 = 32$ is not a perfect square.

Would you like a detailed explanation of how I checked each term?

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1. What are the properties of a perfect square?
2. Can a non-square integer power be a perfect square?
3. How does one verify if a number is a perfect square?
4. Are there other powers of integers that yield perfect squares?
5. Why does an odd exponent generally result in a non-square for non-square bases?

Tip: When evaluating whether a number is a perfect square, look for an integer that, when squared, gives the original number.