Asked by Nicholai
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 5.5 right parenthesis Superscript 0
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Part 1
left parenthesis negative 5.5 right parenthesis Superscript 0equals
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(−5.5)^0 = 1
Two expressions equivalent to this:
- 1
- (−2)^0
- (−5.5)^2 ÷ (−5.5)^2
Why they are equivalent:
- For any nonzero number a, a^0 = 1. One way to see this is a^m ÷ a^m = a^(m−m) = a^0, but the left side equals 1, so a^0 = 1. Here a = −5.5 (which is not zero), so (−5.5)^0 = 1.
- Also, any other nonzero number raised to the 0th power (for example (−2)^0) equals 1, and a ratio like (−5.5)^2 ÷ (−5.5)^2 equals 1 and simplifies to (−5.5)^(2−2) = (−5.5)^0, showing the same result.
Two expressions equivalent to this:
- 1
- (−2)^0
- (−5.5)^2 ÷ (−5.5)^2
Why they are equivalent:
- For any nonzero number a, a^0 = 1. One way to see this is a^m ÷ a^m = a^(m−m) = a^0, but the left side equals 1, so a^0 = 1. Here a = −5.5 (which is not zero), so (−5.5)^0 = 1.
- Also, any other nonzero number raised to the 0th power (for example (−2)^0) equals 1, and a ratio like (−5.5)^2 ÷ (−5.5)^2 equals 1 and simplifies to (−5.5)^(2−2) = (−5.5)^0, showing the same result.
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