1. The problem is to simplify the expression $\frac{8^7}{8^5}$.\n\n2. We use the rule of exponents that states $\frac{a^m}{a^n} = a^{m-n}$ when the bases are the same.\n\n3. Applying this rule, we get $\frac{8^7}{8^5} = 8^{7-5}$.\n\n4. Simplify the exponent: $7 - 5 = 2$.\n\n5. So, $\frac{8^7}{8^5} = 8^2$.\n\n6. Calculate $8^2 = 64$.\n\nFinal answer: $64$.