The expression shown in the image is:

$(-2)^{4^2}$

First, let's break down the expression step by step.

Step 1: Solve the exponent $4^2$

$4^2 = 16$

Step 2: Apply the result to the base $-2$

Now we evaluate $(-2)^{16}$. When raising a negative number to an even exponent, the result is positive.

$(-2)^{16} = 2^{16} = 65,536$

Thus, the value of $(-2)^{4^2}$ is 65,536.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How does the outcome change if the exponent is odd instead of even for a negative base?
2. What happens if you raise a negative number to a fractional power?
3. Can you solve the same expression but with a different base, like $(-3)^{4^2}$?
4. How would the calculation change if there was no parentheses around the base, e.g., $-2^{4^2}$?
5. How do powers of powers, such as $(a^m)^n$, simplify in general?

Tip: When raising negative numbers to powers, always pay attention to whether the exponent is even or odd! Even exponents give positive results, while odd ones keep the base's sign.