1. **State the problem:** Simplify the expression $\frac{7^{34}}{7^{32}}$. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Apply the rule:** $$\frac{7^{34}}{7^{32}} = 7^{34-32}$$ 4. **Simplify the exponent:** $$7^{2}$$ 5. **Calculate the final value:** $$7^{2} = 49$$ **Final answer:** $49$