Last Light Bulb Standing

Question

Suppose you have $10$ independent light bulbs labelled $1-10$ whose lifetime is modelled by $T_i \sim \text{Exp}(1/10)$ for each $1 \leq i \leq 10$. Furthermore, suppose you have an $11$th light bulb whose lifetime is modelled by $X \sim \text{Exp}(1/90)$. Find $\mathbb{P}[X > T_1 + \dots + T_{10}]$. The answer is in the form $q^{b}$, where $0 < q < 1$ is a rational number and $b$ is an integer with $b$ maximal. Find $qb$.