Question

Im struggling to understand what this calculation is return base * power(base, exponent - 1); in the following code. Does base get multiplied with the power function that has the base inside it again?

var power = function(base,exponent){
      if(exponent === 0){
          return 1;
      } else {
          return base * power(base, exponent - 1);
      }
};

power(2,2);

Does this mean that return base = 2*(2,2-1)?

Answer 1

Does base get multiplied with the power function that has the base inside it again?

Yes, absolutely, and that’s how this recursive implementation actually works.

If you expand power(10, 4) for example you get:

power(10, 4)
= 10 * power(10, 3)
= 10 * 10 * power(10, 2)
= 10 * 10 * 10 * power(10, 1)
= 10 * 10 * 10 * 10 * power(10, 0)
= 10 * 10 * 10 * 10 * 1

It should hopefully be clear from this expansion exactly why this is a valid (albeit slow) way to calculate exponents.