There are many methods to calculate for some positive integer k and given x.
The first DIRECT METHOD, just multiplies with itself to find and then multiplies with to find and keeps going like this till is found.
Thus for example to find it requires 3 multiplications: ( with itself to find , with to find and finally with to find .)

On the other hand there is also a second method, the SQUARING METHOD, where we at each stage multiply the last number with itself.
For example to find , one first multiplies with itself to get , then one multiplies with itself to get .
Notice this second method only took 2 multiplications to find .
Answer the following questions:
To calculate with the first direct method takes multiplications.
To calculate with the second, squaring method takes multiplications.

Which method is more efficient for large k?




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