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.