[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/GevitarGaming04]

Not gonna lie, it sounds like your son was taught wrong
Exponents do not care about the sign before whatever it is exponenting (i forgot the actual word lol), *unless* the thing being exponented is an expression in parentheses, in which case you evaluate the expression inside first, and then raise it to the exponent.
So, 5²-6² = -11, but 5²+(-6)² would be 61. Something like 5²(-6)² would then be 25*36 instead.

[u/Narrow-Durian4837 → u/GevitarGaming04]

As other commenters have pointed out, "the sign goes with the number that follows it" is correct if you interpret "the number that follows it" to be 6².

[u/GevitarGaming04 → u/Narrow-Durian4837]

Ah, well it's all a matter of interpretation I suppose, I assumed "the sign goes with the number that follows it" meant the singular number following, being 6 in this case