<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't work like that. In fact, we can'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'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'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't split up the denominator like this.</p>