Skill: Distinguish a negative base from a negative power value

A negative base has the negative sign inside parentheses:

• In $(-3)^2$, the base is $-3$.
• The exponent $2$ means multiply the base by itself:

$$(-3)^2=(-3)(-3)=9$$

A negative power value has the negative sign outside the power:

• In $-3^2$, the base is $3$, not $-3$.
• Find the power first, then apply the negative sign:

$$-3^2=-(3^2)=-(9)=-9$$

So, for the example,

$$(-3)^2=9 \qquad\text{but}\qquad -3^2=-9$$

The parentheses decide whether the negative sign is part of the base. A negative base raised to an even exponent gives a positive result, while a negative base raised to an odd exponent gives a negative result.