Which of the following is FALSE for general nonzero $x$ and $y$?
A$(x^a)(y^a) = (xy)^a$
B$(x + y)^2 = x^2 + y^2$
C$(x^a)^b = x^{ab}$
D$x^0 = 1$
Answer & Solution
Correct answer: B. $(x + y)^2 = x^2 + y^2$
Expanding $(x+y)^2$ correctly gives $x^2 + 2xy + y^2$, so the equality with $x^2 + y^2$ is false (it omits the cross term $2xy$). Each of the other three statements is a standard exponent or identity rule that holds for all permitted bases.
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