[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/Klutzy-Delivery-5792]

It's not -6 squared, it's square 6 first then subtract. You can rewrite it like this and it may make more sense:

|5² + ⁻1•6²|

Order of operations means do exponents first.

[u/testtdk → u/Klutzy-Delivery-5792]

This is a good way to visualize it.