Suppose you have a number r and you need to compute its n-th power, that is, the value rn. We are assuming that n is an integer. For convenience, we can also assume that r is a positive real number, and that n is positive:
We know you could simply enter r into your calculator, and then multiply by r a total of n-1 times to get the answer.
Your calculator might actually have an exponent key, allowing you to compute the result in one step, but we're not going to allow that method. We only want to use "simple" operations like multiplication.
The first hint that there might be a better way comes when you start to compute r10 the regular way. After 4 multiplications, you have r5 in your calculator. Now you realize you can take a shortcut and simply multiply this quantity by itself, computing the answer in 5 steps rather than 9.
I give up, show me the solution.