1. **Problem:** Solve the exponential equation $$7^{2x+8} = 1$$. 2. **Formula and rules:** Recall that for any base $a > 0$, $a \neq 1$, the equation $a^y = 1$ holds if and only if $y = 0$. 3. **Apply the rule:** Set the exponent equal to zero: $$2x + 8 = 0$$ 4. **Solve for $x$:** $$2x = -8$$ $$x = \frac{-8}{2}$$ 5. **Simplify:** $$x = -4$$ 6. **Answer:** The solution to the equation is $x = -4$.