Exponent help

[Benstephens1164]

As I was reviewing my khan academy SAT math questions, I came across this one. I now know that the first two terms equal -1 and 7, and I understand how to get those numbers but I am confused about the -2^2. I tried searching google about this and some sites said that -2^2 could be 4 and other sites said it is -4. I always thought that a negative squared was essentially just a negative times a negative, thus making it a positive answer. Apparently, this is not the case but I was just wondering why it doesn't work like that in this question when all other times in school I have done a negative squared, the outcome was positive. Any help would be greatly appreciated as I have not been able to find out why it is a negative 4.

 

[lev888]

-2^2 could be 4

Just use the precedence rules: exponents first, then subtraction.

 

[Dr.Peterson]

As I was reviewing my khan academy SAT math questions, I came across this one. I now know that the first two terms equal -1 and 7, and I understand how to get those numbers but I am confused about the -2^2. I tried searching google about this and some sites said that -2^2 could be 4 and other sites said it is -4. I always thought that a negative squared was essentially just a negative times a negative, thus making it a positive answer. Apparently, this is not the case but I was just wondering why it doesn't work like that in this question when all other times in school I have done a negative squared, the outcome was positive. Any help would be greatly appreciated as I have not been able to find out why it is a negative 4.








View attachment 23910

In that expression, there is no "square of a negative". It says to subtract the number 2²; so the expression -(5c)⁰ + 7¹ - 2² means -1 + 7 - 4 = 2. If it meant to square -2, then there would be no operation before that!

Even if the expression were just -2², we would take it as -(2²), that is, the negative of the quantity 2 squared. This is, in part, so that the rule is the same as for your example, that we do the negative/subtraction after doing the squaring. So we say that -2² = -4. If we meant to square -2, we would have to write (-2)².

In your example I think it's reasonably clear that the negative is not part of what is being squared; in a standalone -2², it is not so obvious, and you have to remember the rule specifically. As a result, we tend to avoid writing expressions like that.

 

[Benstephens1164]

In that expression, there is no "square of a negative". It says to subtract the number 2²; so the expression -(5c)⁰ + 7¹ - 2² means -1 + 7 - 4 = 2. If it meant to square -2, then there would be no operation before that!

Even if the expression were just -2², we would take it as -(2²), that is, the negative of the quantity 2 squared. This is, in part, so that the rule is the same as for your example, that we do the negative/subtraction after doing the squaring. So we say that -2² = -4. If we meant to square -2, we would have to write (-2)².

In your example I think it's reasonably clear that the negative is not part of what is being squared; in a standalone -2², it is not so obvious, and you have to remember the rule specifically. As a result, we tend to avoid writing expressions like that.

Thank you for the explanation!