Divisible Palindromes

Let n be the number of palindromes consisting only of 1s and 0s that have exactly 2014 digits and are divisible by 11. n can be expressed in the form $a^b$ where $a,b \in \mathbb{N}$ and $a$ is as small as possible but $a \ne 1$ . Find $\dfrac{b}{a}$ . $\textbf{ Details and Assumptions }$ Despite only consisting of 1s and 0s the palindromes are all in base 10