Power Function Oddity

[Eddie W. Shore]

On the Home screen:

4^4^4^4 returns 9.999999999999E499

But
4^4, Enter
Ans^4, Enter
Ans^4, Enter returns answer 3.40282366921E38

Which one is correct?

[DA74254]

I guess it'll be an overflow.
The 3.xxE38 is certainly incorrect.

WolframAlpha claims the answer is a number that contains 8.07E158 digits..
Also, after 10 minutes, my xMaxima has yet not returned any answer..

[DA74254]

Hmm, let me edit my answer a little.
Both *may* be correct. Depending on how you "set up" your expression.

By ^4 for each intermediate calculation, you get a first level exponetiation, whereas, if you "stack" the ^4's you'll get a really high number.

Your latter answer would be 4^4=256^4=4294967296^4=340282366920938463463374607431768211456.

But the "stacking would equal 4^134078079299425970995740249982058461274793658205923933777235614437217640\
300735469768018742981669034276900318581864860508537538828119465699464336490060\
84096

Edit:
Here's the link to WA: https://www.wolframalpha.com/input/?i=4%5E4%5E4%5E4

[Albert Chan]

Exponentiation operator is evaluated from right to left:

4^4^4^4 = 10^(4^4^4 * log10(4)) ≈ 10^8.0723e153

[toml_12953]

(07-22-2019 08:35 PM)Albert Chan Wrote:  Exponentiation operator is evaluated from right to left:

4^4^4^4 = 10^(4^4^4 * log10(4)) ≈ 10^8.0723e153

If it's evaluated right to left, wouldn't it be:

4^(4^(4^4))

which is 4^1.340780792994e+154. Too big for the Prime.

[Carlos295pz]

(07-22-2019 07:37 PM)Eddie W. Shore Wrote:  4^4^4^4 returns 9.999999999999E499

But
4^4, Enter
Ans^4, Enter
Ans^4, Enter returns answer 3.40282366921E38

4^4^4^4 returns 9.999999999999E499

4^4, Enter
4^Ans, Enter
4^Ans, Enter returns answer 9.999999999999E499

[ijabbott]

4^4^4^4 Enter is 4^(4^(4^4)), but 4^4 Enter Ans^4 Enter Ans^4 Enter is ((4^4)^4)^4.

I.e. ^ associates right-to-left, not left-to-right.