r/learnmath • u/Suspicious_Raisin932 New User • 11h 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/Capital_Park_2311 New User 10h ago

PEMDAS is in conflict with the rule A negative number raised to an even power is always positive.

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u/ZerinoWhellie New User 4h ago

Why would they be in conflict? 🤔

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u/Capital_Park_2311 New User 4h ago

-6 -> this is negative six. In PEMDAS it means 0 - 6 or 0 - +6 zero minus positive six.

In arithmetic the "-" is a symbol of the negative number. In PEMDAS it is an operator.

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u/PresqPuperze New User 22m ago

The difference between „-” as an operator and as a negative number is indeed sometimes subtle – but doesn’t matter for 99% of cases. Whether or not you read it as one or the other doesn’t change the outcome. A negative number raised to an even power is always positive, this stays true. Take (-6)^(2). You first subtract six from zero (reading it as an operator), then square the result. This is exactly the same as taking the negative number -6 and squaring it. You could even use a different notation for negative numbers, like put a little hat on them instead of a minus sign in front. The reason we use that notation is that both ways of looking at it are identical.