# A Pre-RMO question! -20

Algebra Level 3

Suppose that $4^{x_1}=5,\space5^{x_2}=6,\space6^{x_3}=7...126^{x_{123}}=127,\space127^{x_{124}}=128$. If the product $x_1x_2x_3...x_{123}x_{124}$ is of the form $\frac{m}{n},\space\gcd(m,n)=1,\space m\in \mathbb Z^+,\space n\in \mathbb Z^+$, find $m+n$.

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