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25 Sep 2019, 11:36
Kudos
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I want to verify these properties of -1,0,1 exponent properties all in one place;
0^X = 0
X^0 = 1
-X^0 = 1
1^1 = 1
X^1 = X
(1/X)^1 = 1/X
1 ^ -1 = 1/1
-1^odd = -1
-1^even = 1
1 ^ -x = 1/x
0^X = 0
X^0 = 1
-X^0 = 1
1^1 = 1
X^1 = X
(1/X)^1 = 1/X
1 ^ -1 = 1/1
-1^odd = -1
-1^even = 1
1 ^ -x = 1/x
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25 Sep 2019, 20:16
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kapstone1996
You are wrong here..
\(x^{-1}=\frac{1}{x}\),
\(1^{-x} = 1\)
26 Sep 2019, 01:24
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To make the identities more clear, i have made some changes.
0^X = 0, Valid if x is not equal to 0
X^0 = 1, Valid if x is not equal to 0
-X^0 = 1, Valid if x is not equal to 0
1^1 = 1, correct
X^1 = X, correct
(1/X)^1 = 1/X, defined when x is not equal to 0
1 ^ -1 = 1/1, correct
-1^odd = -1 correct
-1^even = 1 correct
1 ^ -x = 1, correct
0^X = 0, Valid if x is not equal to 0
X^0 = 1, Valid if x is not equal to 0
-X^0 = 1, Valid if x is not equal to 0
1^1 = 1, correct
X^1 = X, correct
(1/X)^1 = 1/X, defined when x is not equal to 0
1 ^ -1 = 1/1, correct
-1^odd = -1 correct
-1^even = 1 correct
1 ^ -x = 1, correct
kapstone1996
