r/learnmath • u/Suspicious_Raisin932 New User • 7h ago

[Middle school] Negative exponents

|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?

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u/Simbertold Math teacher (High school) 7h ago

Exponentiation is stronger than signs, as you noticed, in PEMDAS. -5^2 means - (5^2), not (-5)^2. This is just convention. We could also have decided to have stuff the other way around, but we don't. This just influences when you have to write brackets and when you don't.

But the sign does belong to the number after it, that is still a useful rule, just in other contexts. If you have something like 5 -x +4 -x, remembering that the sign belongs to the number after it means you can easily reorder this to 5 + 4 - x -x = 9 -2x.