1. **State the problem:** Find the value of $x$ in the equation $$\frac{6^{16} \times 6^{2}}{6^{9} \times 6^{4}} = 6^{x}$$. 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. **Simplify numerator:** $$6^{16} \times 6^{2} = 6^{16+2} = 6^{18}$$. 4. **Simplify denominator:** $$6^{9} \times 6^{4} = 6^{9+4} = 6^{13}$$. 5. **Rewrite the fraction:** $$\frac{6^{18}}{6^{13}} = 6^{18-13} = 6^{5}$$. 6. **Compare with right side:** Since $$\frac{6^{16} \times 6^{2}}{6^{9} \times 6^{4}} = 6^{x}$$ and we found it equals $$6^{5}$$, then $$x = 5$$. **Final answer:** $$x = 5$$