The expression from the image is $81^{\log_3 2}$. Let's solve this step by step.

1. Rewrite 81 as a power of 3. Since $81 = 3^4$, we can express the original problem as: $(3^4)^{\log_3 2}$
2. Apply the power of a power rule: $(3^4)^{\log_3 2} = 3^{4 \cdot \log_3 2}$
3. Use the logarithmic identity $a^{\log_a b} = b$, which simplifies this expression: $3^{4 \cdot \log_3 2} = 2^4 = 16$

Thus, the value of the expression is $\boxed{16}$.

Would you like more details or have any other questions?

Here are five related questions to deepen your understanding:

1. How would you solve $27^{\log_3 5}$?
2. Can you simplify $9^{\log_3 4}$?
3. How do logarithmic properties apply in expressions like $a^{\log_b c}$?
4. What is the general form for simplifying $x^{\log_b y}$?
5. How does the change of base formula help with logarithms?

Tip: Remember that expressing numbers in terms of a common base (like powers of 2 or 3) is often key to simplifying complex expressions with logarithms.