The problem asks us to evaluate the given exponential expressions: $3^3$, $2^5$, $7^4$, $(\frac{2}{7})^3$, and $(\frac{1}{6})^4$.

1. Problem Description

The problem asks us to evaluate the given exponential expressions: $3^3$, $2^5$, $7^4$, $(\frac{2}{7})^3$, and $(\frac{1}{6})^4$.

2. Solution Steps

* Evaluate $3^3$:

$3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27$.

* Evaluate $2^5$:

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 4 \times 4 \times 2 = 16 \times 2 = 32$.

* Evaluate $7^4$:

$7^4 = 7 \times 7 \times 7 \times 7 = 49 \times 49 = 2401$.

* Evaluate $(\frac{2}{7})^3$:

$(\frac{2}{7})^3 = \frac{2^3}{7^3} = \frac{2 \times 2 \times 2}{7 \times 7 \times 7} = \frac{8}{343}$.

* Evaluate $(\frac{1}{6})^4$:

$(\frac{1}{6})^4 = \frac{1^4}{6^4} = \frac{1}{6 \times 6 \times 6 \times 6} = \frac{1}{36 \times 36} = \frac{1}{1296}$.

3. Final Answer

$3^3 = 27$

$2^5 = 32$

$7^4 = 2401$

$(\frac{2}{7})^3 = \frac{8}{343}$

$(\frac{1}{6})^4 = \frac{1}{1296}$