The expression in the image is $(3^4)^5$.

To simplify this, we apply the power of a power rule in exponents, which states:

$(a^m)^n = a^{m \cdot n}$

Thus, $(3^4)^5$ becomes:

$3^{4 \cdot 5} = 3^{20}$

Now, calculating $3^{20}$:

$3^{20} = 3 \times 3 \times 3 \times \ldots \ (\text{20 times}) = 3,486,784,401$

So, $(3^4)^5 = 3^{20} = 3,486,784,401$.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you simplify $(a^m)^n$ if both $a$, $m$, and $n$ are variables?
2. Can you apply the power rule to expressions like $(2^3)^4$? What is the result?
3. How does the power of a product rule differ from the power of a power rule?
4. What happens if the base in the expression is a fraction, such as $\left(\frac{2}{3}\right)^4$?
5. How do you solve problems involving negative exponents?

Tip: When working with large exponents, breaking down the expression using exponent rules helps manage calculations efficiently.