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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 1.9 right parenthesis Superscript 0
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Part 1
left parenthesis negative 1.9 right parenthesis Superscript 0equals
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(−1.9)^0 = 1
Two other expressions equivalent to it: 2^0 and (−3)^0 (both equal 1).
Why: For any nonzero number a, a^0 = 1. Reason: a^m / a^m = a^{m−m} = a^0, but a^m / a^m = 1, so a^0 = 1. Here −1.9 ≠ 0, so (−1.9)^0 = 1.
Two other expressions equivalent to it: 2^0 and (−3)^0 (both equal 1).
Why: For any nonzero number a, a^0 = 1. Reason: a^m / a^m = a^{m−m} = a^0, but a^m / a^m = 1, so a^0 = 1. Here −1.9 ≠ 0, so (−1.9)^0 = 1.
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