Concept: The question tests on the fundamentals of Exponents.
Solution:
Let the value be “x” times the value of 2(−17)
Then 1/5(2-14 + 2-15 + 2-16 + 2-17) = x*2-17
Thus, x = 1/5(2-14 + 2-15 + 2-16 + 2-17) / 2-17
= 2 17 * 1/5( 2-14 + 2-15 + 2-16 + 2-17) [As 2-17 is 1/217 ]
= (23+22+21+20)/5
=15/5 = 3 (option C)