Raising to what power will require more operations?

Question

Mathematics

Raising to what power will require more operations?
88 83 97

Answer 1

88 in binary = 1011000
83 = 1010011
97 = 1100001
That is, we first multiply the number 6 times to get powers 2, 4, 8, 16, 32, 64, then we multiply them together. To do this, you need as many multiplications as there are units in the binary representation of the number. Those. for raising to a power of 88, you will need 6 + 3 = 9 multiplications, for a power of 83 -> 6 + 4 = 10 multiplications, for a power of 97, nine multiplications.
If you calculate through the exponent and the logarithm, then two operations for any degree.