system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: When a calculator resolves 1.001^10000, does it actually multiply 1.001 10000 times in sequence?
gpt
No. What exactly the calculator does depends on the calculator, but it is always quite complex and not very ELI5-friendly.

Typically they will convert a^b to e^(b*ln(a)^) with the natural logarithm ln( ) and the exponential function. Then it can use ln(1+x)=x - x^(2)/2 + x^(3)/3 (and probably more terms, this is called a Taylor series) to find the approximate value of ln(1.001)=0.000999500. Multiply it by 10000: 9.99500

To calculate e^(9.99500) there are similar tricks, and the final result is  about 21900.

That way you don't have to do 10,000 multiplications, and you can also calculate 1.001^10000.35 and similar expressions.