We are given the expression:

$(-3x^2)^3$

Step 1: Apply the Power Rule

The power rule states that $(a^m)^n = a^{m \cdot n}$. Applying this to each term inside the parentheses:

$(-3)^3 \cdot (x^2)^3$

Step 2: Simplify Each Term

• $(-3)^3 = (-3) \times (-3) \times (-3) = -27$
• $(x^2)^3 = x^{2 \cdot 3} = x^6$

Step 3: Final Answer

$-27x^6$

Thus, the simplified expression is:

$\mathbf{-27x^6}$

Would you like more details or another example?

Here are 5 related questions to expand your understanding:

1. Simplify $(2x^3y^2)^4$.
2. Evaluate $(-5a^2b^3)^2$.
3. Simplify $(4m^5n^{-2})^3$.
4. Apply the power rule to $(7x^{-1}y^4)^2$.
5. Expand and simplify $(-2x^2y)^3$.

Tip:

When raising a negative base to an odd exponent, the result remains negative. When raising it to an even exponent, the result becomes positive.