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# Common Misconceptions (Algebra)

Arm yourself with the tools to be the king or queen of heady mathematical debates, like the age old question of whether 0.999.... = 1.

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\[\big(x^2\big)^3 =\, ?\]

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If \(x^5 = 3\), then \[ (2x)^5 =\]

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If \(x = 5\), then \(\sqrt{x^2} = \)

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Which of the following is equal to \(2^{-3}\text{?}\)

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For which choices of \(a\) and \(b\) is the equation \[(ab)^\frac{1}{2} = a^\frac{1}{2}\cdot b^\frac{1}{2}\]

**not** true?

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