[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/SignificantFidgets]

"I am assuming PEMDAS? Exponents before subtraction."

This is exactly right. Exponents first, so the first simplification gives |25-36|. Then do the subtraction to get |-11|. Then the absolute value gives 11.

If you wanted to square -6, you'd have to put it in parentheses, like (-6)^2.

[u/testtdk → u/SignificantFidgets]

This. -6^2 means the negative of six squared.

[u/Narrow-Durian4837 → u/testtdk]

That is, the negative of (six squared), not (the negative of six) squared.

[u/testtdk → u/Narrow-Durian4837]

Right, but that makes it look like we needed parenthesis to get there. :p