Where the Minus Sits

Compare ${\left(-4\right)}^{2}$ with $-{4}^{2}$. In ${\left(-4\right)}^{2}$ the parentheses make -4 the base, so it is $\left(-4\right) \cdot \left(-4\right)$, which is 16. In $-{4}^{2}$ there are no parentheses, and the power touches only the 4. It means the opposite of ${4}^{2}$, so $-{4}^{2}$ is -16.

Why? A power belongs to whatever sits right under its exponent, and it is worked out before anything else in the line, including the minus sign in front. Think of $-{4}^{2}$ as $0-{4}^{2}$: the power goes first, giving $0-16$, and only then is the 16 taken away.

So when you meet a power, look at what is directly under the exponent. A closing parenthesis means the whole bracket is the base, sign included. A digit means only that number is, and any minus in front waits until the power is done.