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Multiple Representations Simplify this expression. Use pencil and paper. Write at least two expressions equivalent to this one. Explain why they are equivalent.
left parenthesis negative 6.1 right parenthesis Superscript 0
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Part 1
left parenthesis negative 6.1 right parenthesis Superscript 0equals
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(−6.1)^0 = 1
Two other expressions equivalent to this are:
- (6.1)^0 = 1
- 100^0 = 1
Why: For any nonzero real number a, a^0 = 1. One way to see this is a^m / a^m = a^{m−m} = a^0, but a^m / a^m = 1, so a^0 = 1 (for a ≠ 0). Note: 0^0 is undefined.
Two other expressions equivalent to this are:
- (6.1)^0 = 1
- 100^0 = 1
Why: For any nonzero real number a, a^0 = 1. One way to see this is a^m / a^m = a^{m−m} = a^0, but a^m / a^m = 1, so a^0 = 1 (for a ≠ 0). Note: 0^0 is undefined.
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