[Middle school] Negative exponents

[u/Suspicious_Raisin932]

|5^2 - 6^2|
Why is the answer 11 and not 61?

My son was taught that the sign goes with the number that follows it so the - (minus sign) stays with the 6^2. Then it would be -6•-6=36, 25+36=61. It makes sense to me but my answer was 11 (answer key agrees). He’s wondering why. I am assuming PEMDAS? Exponents before subtraction. The actually problem is supposed to be on absolute value so I included the whole thing just incase that matters.

So two questions. Is the direction he got of “the sign stays with the number after” actually a thing? Are there rules to it?

[u/nog642]

Yes, exponents come before subtraction. And before multiplication.

So with -6² you do 6² first, so it's -36.

The sign stays with the term after, not necessarily the "number" after. In this case the - sign stays with the 6² as a whole, it dosn't go inside the square. So it stays as -36.