To simplify \((-3u^2 w)^4\), follow these steps:

### Step 1: Apply the power to each factor inside the parentheses.

\[
(-3u^2 w)^4 = (-3)^4 \cdot (u^2)^4 \cdot (w)^4
\]

### Step 2: Calculate each power.
- \((-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81\)
- \((u^2)^4 = u^{2 \times 4} = u^8\)
- \((w)^4 = w^4\)

### Step 3: Combine the results.

\[
81u^8w^4
\]

Thus, \((-3u^2 w)^4 = 81u^8w^4\).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How would you simplify \((2x^3y)^5\)?
2. What happens when you raise a negative base to an odd power?
3. How do you simplify expressions with fractional exponents?
4. How does the distributive property work in exponents?
5. What is the result of \((-4a^3b)^3\)?

**Tip:** Always apply exponents to each factor inside the parentheses when simplifying expressions like this one.

Learn how to simplify the expression (-3u^2 w)^4 by applying exponent rules to each factor. This solution walks through raising powers to powers and calculating the result, making it easy for students in Grades 8-10 to understand.

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