Exponential expressions: coefficients: negative signs

Tutoring math, details can be important. The tutor mentions negative signs in front of exponential expressions.

For situations where superscripts aren’t available, exponents are sometimes indicated with a ^ sign. Therefore, 3^4 = 3*3*3*3 = 81.

Today’s post isn’t about that specifically, but it’s a notation one might see.

Today’s post, rather, is about the idea that -3^2 = -9, but (-3)^2 = 9.

The reason is the order of operations (BEDMAS): in the expression -3², the exponent is evaluated first, while the subtraction is done afterwards. Since there are no brackets, the exponent is only on the 3, not the -. The expression can be imagined as (-1)x3².

With (-3)², the exponent is on both the negative and the 3, so we have (-3)(-3) = 9.

In my experience, some calculators auto-bracket, so when one tries to enter, for instance, -5², the calculator automatically changes it to (-5)², then gives the answer 25. It’s good to watch the calculator’s screen and be aware of what it’s doing.