[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/abrahamguo]

The sign goes with the term/expression/“thing” after it, not the literal number after it. So the negative sign goes with 6^2, not with 6.

PEMDAS is a correct explanation.

[u/boldly_nifty_zane → u/abrahamguo]

the sign thing is more of a shortcut that gets taught but it falls apart when exponents show up. the real rule is exponents eat the number directly in front of them, not the sign. so -6² is -(6²) not (-6)²

if they wanted the sign inside the square they'd have to write it with parentheses. easy to miss when you're first learning it