VTMO 2026 - Grade 7 - Semifinal - SET 3 - Self-study Question 19

Let $a,b,c\in\mathbb Z$ satisfy $\dfrac{4^4\times5^5\times6^6}{8^8\times9^9\times10^{10}}=2^a\times3^b\times5^c$. Find $a-b+c$.