https://file.aiquickdraw.com/mathbot/file/1726450281822hqiz1bqk.jpg

The expression provided in the image is:

\[
(-2v^{12})^2
\]

### Simplification Steps:

1. Apply the exponent to both parts inside the parentheses:
   \[
   (-2)^2 \cdot (v^{12})^2
   \]

2. Simplify each part:
   - \((-2)^2 = 4\)
   - \((v^{12})^2 = v^{24}\) (use the rule \((a^m)^n = a^{m \cdot n}\))

3. The fully simplified expression becomes:
   \[
   4v^{24}
   \]

### Final Answer:
\[
4v^{24}
\]

Would you like any additional details on the steps?

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Here are some follow-up questions:
1. What is the rule for simplifying expressions with exponents?
2. How do you handle negative bases raised to an even power?
3. Can you explain why \(v^{12}\) squared becomes \(v^{24}\)?
4. What happens when a negative number is raised to an odd power?
5. How do you simplify expressions with multiple variables?

**Tip:** Always apply the exponent to both the coefficient and the variable separately when dealing with terms like \((-2v^{12})^2\).

Simplify the following expression completely: (-2v^12)^2

Learn how to simplify the expression (-2v^12)^2 using exponent rules. The problem involves key algebraic concepts such as exponentiation, multiplication of powers, and handling negative coefficients. Suitable for students in Grades 8-10.

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