A number $x$ factors as $107\cdot109^5$, and $107$ and $109$ are primes. What is the exponent of $109$ in the prime factorization of $x^{11}$?
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You are a helpful assistant.<|im_end|>
<|im_start|>user
A number $x$ factors as $107\cdot109^5$, and $107$ and $109$ are primes. What is the exponent of $109$ in the prime factorization of $x^{11}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
55
A number $x$ factors as $107\cdot109^5$, and $107$ and $109$ are primes. What is the exponent of $109$ in the prime factorization of $x^{11}$?
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