Link: Tricky Rational Exponents

Consider the following apparent paradox:

$-1 = (-1)^1 = (-1)^\frac{2}{2} = (-1)^{2 \cdot \frac{1}{2}} = ((-1)^2)^\frac{1}{2} = (1)^\frac{1}{2} = \sqrt{1} = 1$

Of the seven equalities in this statement, exactly which of them are false? Give a specific number between (1) and (7). Join in the discussion where I posted this at StackExachange, if you like:

StackExchange:
What are the Laws of Rational Exponents?