From the question we were told that 2^13 is approximately equal to 8000. We are asked to find the best approximation for 2^26.
In this question, we will have to use the formulas of power addition given by:
If we have:
x^a * x^b = x^a+b
(x^a)^b = x^ab
So now let's consider the scenario we are given.
recall, the best appriximation o 2^13 is 8000.
Then the best approximation for 2^26.
Now we have: 26 = 13 * 2
So, we can we can have:
2^13 ------ 8000
squaring both side:
(2^13)^2 --------- (8000)^2
= (2)^13*2 --------- 64000000
= 2^26 -------- 64000000
Therefore,
2^26 = 64,000,000 (best approximation).