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The problem you provided can be solved using limit properties. We are asked to find:

\[
\lim_{{x \to 2}} \left[g(x)\right]^3
\]

### Given Information:
- \(\lim_{{x \to 2}} f(x) = 4\)
- \(\lim_{{x \to 2}} g(x) = -2\)
- \(\lim_{{x \to 2}} h(x) = 0\)

### Solution:
From the limit property \(\lim_{{x \to c}} [g(x)]^n = \left(\lim_{{x \to c}} g(x)\right)^n\), we know that we can apply the limit directly inside the cubic function.

Thus, we have:
\[
\lim_{{x \to 2}} \left[g(x)\right]^3 = \left(\lim_{{x \to 2}} g(x)\right)^3
\]

Since \(\lim_{{x \to 2}} g(x) = -2\), we can substitute this value:
\[
\left(\lim_{{x \to 2}} g(x)\right)^3 = (-2)^3 = -8
\]

### Final Answer:
\[
\lim_{{x \to 2}} \left[g(x)\right]^3 = -8
\]

Let me know if you'd like further details or explanations.

Here are 5 related questions to deepen your understanding:
1. How would the answer change if \(\lim_{{x \to 2}} g(x)\) were positive?
2. What would happen if we had \(\lim_{{x \to 2}} g(x) = 0\)?
3. How does the limit property apply to other powers like squares or fourth powers?
4. Can you generalize this for any continuous function \(g(x)\) as \(x \to a\)?
5. How does the limit of a product of two functions behave under multiplication?

**Tip:** Always check if the function inside the limit is continuous at the point you're evaluating; this often allows you to substitute values directly.

Given that lim(x→2)f(x)=4, lim(x→2)g(x)=-2, and lim(x→2)h(x)=0, find lim(x→2)[g(x)]^3.

This solution explores finding lim(x→2)[g(x)]^3 using limit laws. With the information that lim(x→2)f(x)=4, lim(x→2)g(x)=-2, and lim(x→2)h(x)=0, the answer is computed as -8. Suitable for students in Grades 10-12.

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