To evaluate the expression $\log_3 3^8$, we can apply the logarithmic property:

$\log_b (b^x) = x$

In this case, $b = 3$ and $x = 8$. Therefore,

$\log_3 3^8 = 8$

Thus, the value of the expression is $8$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is $\log_2 2^5$?
2. How do you simplify $\log_4 4^6$?
3. What is $\log_{10} 10^3$?
4. Can you explain the general formula for $\log_b (b^x)$?
5. What is the value of $\log_5 5^9$?

Tip: Always remember that $\log_b (b^x) = x$, which simplifies logarithmic expressions involving powers of the base.