1. **State the problem:** We need to find how many times the value of $2^{-17}$ is contained in the expression $$\frac{2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}}{5}.$$ 2. **Recall the property of exponents:** For any base $a$ and exponents $m,n$, $$a^m = a^n \times a^{m-n}.$$ This allows us to express all terms in the numerator as multiples of $2^{-17}$. 3. **Rewrite each term in the numerator as a multiple of $2^{-17}$:** $$2^{-14} = 2^{-17} \times 2^{3} = 2^{-17} \times 8,$$ $$2^{-15} = 2^{-17} \times 2^{2} = 2^{-17} \times 4,$$ $$2^{-16} = 2^{-17} \times 2^{1} = 2^{-17} \times 2,$$ $$2^{-17} = 2^{-17} \times 1.$$ 4. **Sum the terms:** $$2^{-14} + 2^{-15} + 2^{-16} + 2^{-17} = 2^{-17} (8 + 4 + 2 + 1) = 2^{-17} \times 15.$$ 5. **Divide by 5:** $$\frac{2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}}{5} = \frac{2^{-17} \times 15}{5} = 2^{-17} \times 3.$$ 6. **Interpret the result:** The expression equals $3$ times $2^{-17}$. **Final answer:** C. 3