Let's simplify the expression step by step:

We are given:

$(-3x^3yz^2)(-3^3yz^3)^3$

Step 1: Simplify the exponent part $(-3^3yz^3)^3$

First, calculate $(-3)^3$:

$(-3)^3 = -27$

Now, the expression becomes:

$(-3x^3yz^2)(-27(yz^3)^3)$

Step 2: Apply the power of a product rule to $(yz^3)^3$

$(yz^3)^3 = y^3z^9$

So, we now have:

$(-3x^3yz^2)(-27y^3z^9)$

Step 3: Combine the terms

Now, let's multiply the constants and combine like terms:

$(-3)(-27) = 81$

$x^3y \cdot y^3 = x^3y^4$

$z^2 \cdot z^9 = z^{11}$

So the simplified expression is:

$81x^3y^4z^{11}$

Final Answer:

$81x^3y^4z^{11}$

Would you like a more detailed breakdown or further clarification on any step?

Here are 5 related questions:

1. How do you apply the power of a product rule in exponentiation?
2. What happens when you multiply terms with the same base but different exponents?
3. How do you handle negative signs in multiplication?
4. Can you explain the process of combining variables with exponents?
5. How do you deal with exponents when multiplying polynomials?

Tip: When multiplying terms with the same base, always add the exponents. This rule helps simplify many algebraic expressions.