To determine which of the given options is correct, we can simplify each expression using the properties of exponents.
A. \( \frac{5^8}{5^6} = 5^{8-6} = 5^2 = 25 \) ✔️ (This is correct)
B. \( \frac{3^6}{3^4} = 3^{6-4} = 3^2 = 9 \). So, \( \frac{3^6}{3^4} \neq \frac{1}{9} \). ❌ (This is incorrect)
C. \( \frac{6^7}{6^{-5}} = 6^{7 - (-5)} = 6^{7 + 5} = 6^{12} \). \( 6^{12} \neq 36 \). ❌ (This is incorrect)
D. \( \frac{4^0}{4^3} = \frac{1}{4^3} = \frac{1}{64} \). \( \frac{4^0}{4^3} \neq 0 \). ❌ (This is incorrect)
The only correct statement is A: \( 5^8/5^6 = 25 \).