Bowers' Arrays III

Number Theory Level 3

What is the value of the Bowers' array { 1 , 10 , 10 } \{ 1,10,10\} ?

Note: Bowers' Arrays are a fairly obscure notation. An explanation of them can be found here.


The answer is 1.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

As none of the rules alter the value of the first entry in the array, and Rule 1 defines { a , b } \{ a,b\} = a b a^ b , the final value of this array must be 1 x 1^x where x x is a very complex Bowers' array.

Hence, the answer is simply 1 x 1^x = 1 \boxed{1} .

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1^10^10 = 1

from {a,b} = a^b

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