What is the answer to -6^2?
I would assume 36, but the lesson says that since there are no parenthesis around the 6, it becomes a -36. Why am I not remembering this from pre-algebra?
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Yes, it’s ambiguous. The square of -6 is +36 (negative times negative equals positive), but this is better written with parentheses: (-6)^2 = 36. As given the negative sign could be taken to mean square the number first, then negate it: -6^2 = -(6^2) = -36. I’d seek clarification.
The book is right! Remember order of operations, often referred to as PEMDAS. The acronym means parenthesis, exponent, multiplication, division, addition, subtraction. The squared is an exponent, and the negative is technically multiplication (it’s the same as multiplying by negative 1). Note that exponent comes before multiplication, meaning that exponentiation occurs first in the absence of parenthesis. So first you square the 6 and get 36, and then you apply the negative sign: -36.
Thanks Mariah! Had to read it a few times but I got it. If it was rewritten it would look like
-1×6^2, right? I use PEMA instead of PEMDAS cause…well when my son was 3 that’s how he said….never mind!
Yeah, rewriting it like that is definitely one way to straighten out any confusion.
I like your idea of using PEMA because PEMDAS has an ambiguity that causes a lot of issues for people. For example:
6 – 2 * 0 + 3
You’d start with the multiplication:
6 – 0 + 3
But looking at the PEMDAS acronym, you might now be tempted to give the addition priority over the subtraction because it comes first in the acronym. This is not what you should do; addition and subtraction have equal priority, and when given both, you must move from left to right. The correct method would yield an answer of 9 while the incorrect method would get you 3.
The same is true of multiplication and division.
If it were written -x^2 I don’t think there’d be any confusion (the negative OF x^2). Somehow using a numeric constant instead of a variable seems more confusing (to me). I agree with @Mariah‘s rules for order of operations.
The exponent is evaluated before the negative sign in algebra…
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