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?

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 $(-2v^{12})^2$.