\(\frac{5^6.8-5^7}{5^8-7.5^6}\)
\(=\frac{5^6.8-5^6.5}{5^6.5^2-7.5^6}\)
\(=\frac{5^6\left(8-5\right)}{5^6\left(25-7\right)}\)
\(=\frac{5^6.3}{5^6.18}=\frac{3}{18}=\frac{1}{6}\)
\(\frac{5^6.8-5^7}{5^8-7.5^6}=\frac{5^6.\left(1.8-5\right)}{5^6.\left(5^2-7\right)}=\frac{5^6.3}{5^6.18}=\frac{5^6.3}{5^6.3.6}=\frac{1}{6}\)