1. The problem is to evaluate the expression $6^{6^6}$. 2. This is an example of a power tower or tetration, where the exponent itself is an exponentiation. 3. According to the order of operations, exponents are evaluated from the top down, so first calculate the exponent $6^6$. 4. Calculate $6^6$: $$6^6 = 6 \times 6 \times 6 \times 6 \times 6 \times 6 = 46656$$ 5. Now the expression becomes $6^{46656}$. 6. This number is extremely large and cannot be simplified further in a meaningful way without a computer. 7. So the final answer is $6^{46656}$, which is a very large number.