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https://math.stackexchange.com/questions/2807156/how-can-i-prove-this-operation-on-domino-tilings-is-associative

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e^{2}eeeeeeeeeeeeeeeeee
Multiply e and e to get e^{2}.
e^{3}eeeeeeeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
e^{4}eeeeeeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
e^{5}eeeeeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.
e^{6}eeeeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.
e^{7}eeeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.
e^{8}eeeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.
e^{9}eeeeeeeeeee
To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.
e^{10}eeeeeeeeee
To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.
e^{11}eeeeeeeee
To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.
e^{12}eeeeeeee
To multiply powers of the same base, add their exponents. Add 11 and 1 to get 12.
e^{13}eeeeeee
To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.
e^{14}eeeeee
To multiply powers of the same base, add their exponents. Add 13 and 1 to get 14.
e^{15}eeeee
To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.
e^{16}eeee
To multiply powers of the same base, add their exponents. Add 15 and 1 to get 16.
e^{17}eee
To multiply powers of the same base, add their exponents. Add 16 and 1 to get 17.
e^{18}ee
To multiply powers of the same base, add their exponents. Add 17 and 1 to get 18.
e^{19}e
To multiply powers of the same base, add their exponents. Add 18 and 1 to get 19.
e^{20}
To multiply powers of the same base, add their exponents. Add 19 and 1 to get 20.