Question

Challenge  Is the value of the expression left parenthesis StartFraction 1 Over 5 Superscript negative 2 EndFraction right parenthesis Superscript 0
greater than​ 1, equal to​ 1, or less than​ 1? Use pencil and paper. If the value of the expression is greater than​ 1, show how you can change one sign to make the value less than 1. If the value is less than​ 1, show how you can change one sign to make the value greater than 1. If the value is equal to​ 1, show how you can make one change to make the value not equal to 1.
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Part 1
The value of the expression is
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Answer 1

The expression (1/5^{-2})^0 = 1 because any nonzero number to the 0 power equals 1 (here 1/5^{-2} = 25, which is nonzero).

One single change that makes the value not equal to 1: change the exponent 0 to −1.
Then (1/5^{-2})^{-1} = 25^{-1} = 1/25, which is less than 1.
(If you instead change the 0 to 1 you get (1/5^{-2})^1 = 25, which is greater than 1.)