What were the mathematical techniques used for estimating euler number e upto 18 trillion trillion digits ??

Question

While surfing, I came across this mathematical term: $$(1+9^{-4^{6*7}})^{3^{2^{85}}}$$ which approximately equals to the mathematical constant e (Euler's number) upto 18 trillion trillion digits.

What were the mathematical techniques used to approximate e upto 18 trillion trillion digits ?? What were the mathematical techniques used in finding the term $(1+9^{-4^{6*7}})^{3^{2^{85}}}$??

Answer 1

Hint:

$$\lim_{x \to \infty} (1+1/x)^x = e$$

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Hint 2:

$$\frac{1}{9^{-4^{6*7}}} = 3^{2^{85}}$$

Also, watch this video by Numberphile on the topic