It seems like you're asking about "unique powers" in a mathematical context, but the request is a bit ambiguous. Here are two potential interpretations and explanations:
1. Unique Powers of a Number
In mathematics, unique powers can refer to the powers of a number that are distinct. For example, if we take the base number 2:
- \(2^1 = 2\)
- \(2^2 = 4\)
- \(2^3 = 8\)
- \(2^4 = 16\)
All these results are unique values, as each power gives a different outcome.
2. Powers of Different Bases
If you want unique powers across different bases, consider:
- \(3^2 = 9\)
- \(4^2 = 16\)
In this case, both numbers are unique powers, yielding 9 and 16 from different base numbers.
Clarification Needed
If you intended something different (like a unique application of powers, unique integers raised to powers, or a specific mathematical theorem), please provide additional context so I can assist you better!
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