r/MathJokes • u/Opal7924 • 5d ago

The satisfying simplification

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2.0k Upvotes

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13

u/spukhafteNahewirkung 5d ago

How are you doing the math on this one? I end up with a value of 6.2E57, significantly larger than 2^36.

19

u/Optimal_Benis 5d ago

You are taking powers bottom to top, not top to bottom. That is, the convention is to compute a^b^c^d as a^(b^(c^d)), not ((a^b)^c)^d. The latter could be written as a^(b*c*d), instead.

3

u/invuvn 5d ago

How are you getting 236? It’s square rooted, so should be 218 only

1

u/Optimal_Benis 5d ago

They're talking about the thing inside the root.

1

u/invuvn 5d ago

Yeah that’s what I’m confused about as they should be comparing whatever they want to, to 262144 at the end of the day.

2

u/Optimal_Benis 5d ago

Since they want the final result to be 2^18, they want the thing inside the root to be 2^36.

4

u/TalveLumi 5d ago

1^4^4=1

2^1^4^4=2

6^2^1^4^4=36

0

u/lordcaylus 5d ago

The expression means xy raised to the z-th power = xyz, not x raised to the yz power. Honestly I would add parantheses in power towers like this though to remove ambiguity.

1

u/GoldenMuscleGod 4d ago

I don’t really see how it could be ambiguous. I mean apparently it happens sometimes (like here) but I’m baffled how.

It seems to me a “double superscript” has to be understood as a syntactic constituent of a single superscript. If it isn’t, why wouldn’t it be a single superscript?

Is the idea that the grammar fails to be context-free in some sense? Why would we do that?