###### Example2.1.17

Evaluate $$x^2$$ if $$x=-2\text{.}$$

We substitute:

\begin{align*} x^2\amp=(\substitute{-2})^2\\ \amp=4 \end{align*}

If we don't use parentheses, we would have:

\begin{align*} x^2\amp=-2^2\amp\text{incorrect!}\\ \amp=-4 \end{align*}

The original expression takes $$x$$ and squares it. With $$-2^2=-4\text{,}$$ the number $$-2$$ is not being squared. Since the exponent has higher priority than the negation, it's just the number $$2$$ that is being squared. With $$(-2)^2=4$$ the number $$-2$$ is being squared, which is what we would want given the expression $$x^2\text{.}$$

So it is wise to always use some parentheses when substituting in any negative number.

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