https://file.aiquickdraw.com/mathbot/file/1727812168893rqjlw7i7.jpg

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.

Learn how to solve the exponential expression (-2)^{4^2} step-by-step. Explore key mathematical concepts such as exponents and the order of operations, with a clear explanation of exponent rules. Suitable for students in Grades 8-10.

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