## Finding result of calc with upto 14 digits exponent

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Snake606
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### Finding result of calc with upto 14 digits exponent

I want to know if I have 123 (base) ^ (raised to power) 14 digits exponent number, how can i do it? Currently mathematica is supporting only 9 digits in raised to power but i need calculation for raise to power 14. Is there any method or trick available to calculte such big calculation? If it is possible to calculate raise to power by diving the number and then by adding the results generated from divided calculations to generate the final result.

For example ;

123 ^ 18647575872211 (How to do such calculation)

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### Re: Finding result of calc with upto 14 digits exponent

I'm not familiar with mathematica but given that there's 39 trillion digits in the product, you would need a lot of memory or drive space for that. I doubt it's possible to do the computation in any reasonable amount of time.

Nicias
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### Re: Finding result of calc with upto 14 digits exponent

Why are you trying to do this? You will have more success solving your problem a different way.

gmalivuk
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### Re: Finding result of calc with upto 14 digits exponent

Snake606 wrote:I want to know if I have 123 (base) ^ (raised to power) 14 digits exponent number, how can i do it? Currently mathematica is supporting only 9 digits in raised to power but i need calculation for raise to power 14. Is there any method or trick available to calculte such big calculation? If it is possible to calculate raise to power by diving the number and then by adding the results generated from divided calculations to generate the final result.

For example ;

123 ^ 18647575872211 (How to do such calculation)
I cannot imagine any possible application where you need all 39 trillion digits of the answer, and as you can see, Wolfram Alpha handles an approximate calculation just fine.

If you want to get that result in Mathematica, remember that log10(123^18647575872211) = 18647575872211*log10(123). (In Mathematica, logb(x) is calculated with the input Log[b,x], so an approximate value for this number is given with 18647575872211 Log[10, 123.], as the decimal point means the result will be numerically approximated.)

The result Mathematica gives for that is 3.897166413128775*10^13. (There are commands to specify the number of digits to show, but this is the number I get when I copy and paste the result. On the screen it shows only 3.897167x1013.)

The integer part of that exponent is 38971664131287, which is also what Wolfram Alpha has in the exponent of its scientific notation. If you remember your logarithms again, you know that log(x*y) = log(x) + log(y), so our above result, log10(123^18647575872211), is
3.897167 * 1013 = log10(x * 1038971664131287) = log10(x) + log10(1038971664131287) = log10(x) + 38971664131287

18647575872211*log10(123) - 38971664131287 = N[18647575872211 Log[10, 123] - 38971664131287,10] = 0.7580418369
(In Mathematica, N[x,d] gives a numerical approximation for x to d digits.)

10^(0.7580418369) = 5.72851, which is the beginning of the scientific notation result from Wolfram Alpha.
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mathmannix
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### Re: Finding result of calc with upto 14 digits exponent

Does it help to know that they add up to a multiple of 9?
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