What is the condition for $(\text{number}^c)^b=\text{number}^{cb}$ to be true?
I can't find it on google.ze so I asked it here on math.stackexchange.com.
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For positive real numbers it's always true. Counterexample for negative numbers: $((-1)^2)^{1/2} = 1^{1/2}=1$ but $(-1)^{2\cdot 1/2} = (-1)^1 = -1$.
Hans Lundmark
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you write $1^{1/2}=1$. But also $1^{1/2}=-1$ doesn't look wrong to me :) – Heitor Fontana Feb 05 '14 at 09:53
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1$1^{1/2}=-1$ looks very wrong to me since $x^{1/2}=\sqrt{x}\geq0$ – PrinciPia Feb 05 '14 at 12:34