Given a real number x and a positive integer k, determine the number of multiplications used to find x2k starting with x and successively squaring (to find x2, x4, and so on). Is this a more efficient way to find x2k than by multiplying x by itself the appropriate number of times?

The use of

is a more efficient way to multiplying than starting with x and successively squaring

Given:

real number = x

positive integer = k

Starting with x and squaring to find x², x⁴, xⁿ

The efficient way of multiplying is

where, k = 1, 2, 3, 4,.....…

check:

when k = 1

= x²

when k = 2

= x⁴

when k = 3

=

=

Therefore,

is a more efficient way to multiplying.

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It is a more efficient way to find x2k than by multiplying x by itself the appropriate number of times.

Step-by-step explanation: Please find the attached file for the solution

linear pair postulates