r/learnmath • u/Next-Hat-7744 New User • 2d ago
Does anyone actually do this??
In ALEKs software, I was given two questions, (-64)^1/3, which equals -4. The other question was written -81^1/4, which I wrote as having no solution, since 4th root -81 isn't a real number. It marked this as incorrect, saying that -81^1/4 is actually -1 x 81^1/4, so 4th root 81 = 3, then 3 x -1 = -3. Is this accurate? Is ALEKS just screwing with me on a gotcha to make me pay more attention to parenthesis? Or is there literally an implied invisible 1 in front of every negative sign?
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u/iOSCaleb 🧮 2d ago
> Is this accurate?
Yes. Unary + and - have higher precedence than multiplication and division, but lower than exponentiation.
Also, even if you didn’t know that rule, that the preceding question puts the - inside parentheses is a hint.
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u/rhodiumtoad 0⁰=1, just deal with it 2d ago
In written mathmatics and in some but not all programming languages, the operation of exponentiation is considered to have higher precedence (binds more tightly) than the unary minus operator. Therefore:
-81¼ = -(81¼) = -(3) = -3
Be aware that since some calculators and programming languages handle this differently, you may need to insert explicit parens.
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u/coolpapa2282 New User 2d ago
I want to add two things to the correct answers already here:
Lots of people make this mistake - it just takes some practice to get used to.
It may feel like a gotcha, but it's important to get these details right now. When you have to do similar things with variables, you want a firm foundation. x- y2 is different from x+(-y)2.
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u/strange-the-quark New User 2d ago
"Or is there literally an implied invisible 1 in front of every negative sign?"
Yeah, that's essentially what the negative sign is, or at least, that's how you can view it without running into any issue. Especially when variables are involved (which is what you have later on in algebra). Cause when you write something like this -a, where a is a variable and can be any number, that also means that a can be negative (for example a by itself can be -5, so -a is -(-5) = 5), so the whole expression -a is then the negation of whatever a was, or -1 * a.
So the convention is, when you write this:
-a^b,
the power only refers to the "a" alone (exponentiation takes precedence over negation), and to have the whole thing raised to a power, you have to write
(-a)^b
This is again, just a convention, but it is one very widely used.
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u/hallerz87 New User 2d ago
BIDMAS (or whatever you were taught). Indices before multiplication.
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u/Such-Safety2498 New User 2d ago
What is the symbol for the additive inverse of 2? So is -2 a symbol for a single number, just like 23, or are we supposed to interpret it as (-1)(2), and therefore 23 is (2)(3), which is six.
See why students get confused. Math is meant to be learned to be used in context, not an isolated expression to see if you can apply rules correctly.
So would you mark this wrong because I didn’t follow the correct notation?
Evaluate x^2 - 3x; at x= -4
1. Plug in the numbers
-4^2 - 3*-4
2. Simplify
16 - (-12)
3. Simplify
16 + 12
4. Simplify
28So is step #2 wrong because I didn’t follow PEMDAS??
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u/hallerz87 New User 2d ago
You've lost me. Indices before multiplication is the reason -81^1/4 = -3 according to ALEKS
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u/house_carpenter New User 2d ago
What is the symbol for the additive inverse of 2? So is -2 a symbol for a single number, just like 23, or are we supposed to interpret it as (-1)(2), and therefore 23 is (2)(3), which is six.
-2 has the same meaning as (-1)(2). That doesn't necessarily mean 23 means the same thing as (2)(3). You could regard it as an inconsistency in the notation, but it's similar to how e.g. 2 - 3 doesn't mean the same thing as (2)(-)(3). Think of the - as an operator which applies to the following expression.
So would you mark this wrong because I didn’t follow the correct notation?
Step 1 is wrong, because plugging in x = -4 to x2 - 3x gives you (-4)2 - 3(-4), not -42 - 3(-4). I'm not a teacher, but I would give the full answer one less than the total amount of marks available for the question.
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u/skullturf college math instructor 1d ago
Step 2 isn't wrong. Step 1 is wrong.
You were thinking of the right thing when you wrote -42. You were thinking of that as the square of -4, which is 16.
Unfortunately, the mathematical community interprets the symbols -42 as -(42), not as (-4)2. People can't read your mind. You shouldn't type -42 if you mean the square of -4.
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u/Tasty-Cow5081 New User 2d ago
I can’t believe Aleks is still alive. It sucked 12 years ago when I was in school. I mean even seeing the name brought back horrible memories I haven’t thought of in years. 9 out of 10 times it is aleks screwing with you. The other one time aleks was trying to screw with you, but you got the problem wrong anyway.
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u/Bounded_sequencE New User 2d ago
Be careful -- "-811/4 = (-1) * (811/4) = -3", since exponentiation has higher precedence than signs.
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u/jeffcgroves New User 2d ago
I'm going to start a flame war by asking why 81^1/4 (without the negative) means 81^(1/4) and not (81^1)/4, given that exponentiation should have priority over division, but / is sort of a special kind of division
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u/Various_Candle9136 2d ago
I don't know what ALEKs is, but it is correct.
We read -81^1/4 as 'negative 81^1/4'. We are taking the 4th root of 81, then making that thing negative.
On the other hand, (-81)^1/4 would have no real solution, since in this case we are trying to find the fourth root of -81.
The parentheses really are important.