Common Exponent Mistakes

<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-common-exponent-mistakes">Common Exponent Mistakes Exercise</a></p><p><strong>Mistake 1:</strong> $x^{a}y^b \neq (xy)^{a+b}$<br /> It seems logical, but it just doesn&#39;t work like that. In fact, we can&#39;t really rewrite this in any way since both the bases and exponents are different.</p> <p><strong>Mistake 2:</strong> $(x^a)^b \neq x^{a}x^b$<br /> In this case, you&#39;re supposed to multiply the powers together, to become $x^{ab}$.</p> <p><strong>Mistake 3:</strong> $(x+y)^a \neq x^{a}+y^a$<br /> This is a very common mistake. It should be $(x+y)(x+y)(x+y)...$ applied $a$ times.</p> <p><strong>Mistake 4: </strong>$(-x)^2 \neq -x^2$<br /> It should be $-x \times -x$ and the negatives will cancel to produce $x^2$.</p> <p><strong>Mistake 5:</strong> $\sqrt{x^{2}+y^{2}} \neq x+y$<br /> You can&#39;t square root like this when things are being added together.</p> <p><strong>Mistake 6:</strong> $\frac{a^2}{x+y} \neq \frac{a^2}{x} + \frac{a^2}{y}$<br /> We can&#39;t split up the denominator like this.</p>