There are many methods to calculate x^2^k for some positive integer k and given

Question

There are many methods to calculate x^2^k

for some positive integer k and given x.
The first DIRECT METHOD, just multiplies x with itself to find x^2 and then multiplies x with x^2 to find x^3 and keeps going like this till x^2^k is found.
Thus for example to find x^4 it requires 3 multiplications: ( x with itself to find x^2, x with x^2 to find x^3 and finally x with x^3 to find x^4.)
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 x^4, one first multiplies x with itself to get x^2, then one multiplies x^2 with itself to get x^4 .
Notice this second method only took 2 multiplications to find x^4.


Answer the following questions:

a)To calculate x^16 with the first direct method takes _____ multiplications
b)To calculate x^16 with the second, squaring method takes _____ multiplication

Explanation / Answer

a) 15

b) 3

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