We are asked to evaluate the expression $\frac{3^{400} + 3^{401} + 3^{402}}{3^{400}}$.

1. Problem Description

We are asked to evaluate the expression $\frac{3^{400} + 3^{401} + 3^{402}}{3^{400}}$.

2. Solution Steps

We can rewrite the numerator by factoring out $3^{400}$.

$3^{400} + 3^{401} + 3^{402} = 3^{400} + 3^{400} \cdot 3^1 + 3^{400} \cdot 3^2$.

Factoring out $3^{400}$, we get:

$3^{400}(1 + 3^1 + 3^2) = 3^{400}(1 + 3 + 9) = 3^{400}(13)$.

Now we can rewrite the original expression:

$\frac{3^{400} + 3^{401} + 3^{402}}{3^{400}} = \frac{3^{400}(13)}{3^{400}}$.

We can cancel the $3^{400}$ term from the numerator and denominator:

$\frac{3^{400}(13)}{3^{400}} = 13$.

3. Final Answer

13