Algebra: Negative Constant with an Exponent

How do you interpret this term: -4²

(please note that there is no space between the minus sign and the constant, also there is no parenthesis)

Is it read as "negative four squared", thereby equaling 16?

Or, is it read as "the negative of the product of four squared", thereby equaling -16?

Is it the SPACING that makes the difference?
(I mean the fact that the negative sign butts right up to the constant)

Great question. As you've noted, this is a little ambiguous. Personally, I'd never write -4² alone...I might write it as part of an expression,like 3²-4², which would equal 9 -16 = 7. But if I were forced to interpret it, I'd say it's equal to -16. You do the squaring first, because that's an Exponent in PEMDAS. Then you do the - sign, because that's "multiplication by -1", or "subtraction from zero". Either way, it's later than exponents.

The better things to write are -(4²) or (-4)², which are -16 and +16, respectively. Parentheses make life easier! Math teachers have a tough time reading out (-x)² versus -x²...they'll say "negative x.......*long pause* squared" for the first, and "negative....*long pause*....x squared" for the second. And with variables, it's really not ambiguous at all...-x² is ALWAYS equal to -1 times x squared.

it means -16
Math should be unambiguous. 16 would have been (-4)² - this means that -1 times 4 both squared.

Hope it helps

-4 times -4 would equal 16