1. **State the problem:** Simplify the expression $$\frac{7^8 \times 7^3 \times 7^4}{7^9 \times 7^5}$$. 2. **Recall the exponent rules:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply multiplication rule to numerator:** $$7^8 \times 7^3 \times 7^4 = 7^{8+3+4} = 7^{15}$$. 4. **Apply multiplication rule to denominator:** $$7^9 \times 7^5 = 7^{9+5} = 7^{14}$$. 5. **Apply division rule:** $$\frac{7^{15}}{7^{14}} = 7^{15-14} = 7^1 = 7$$. **Final answer:** $$7$$.