To simplify \((-3x^4 y)^5\), we'll apply the power of a product rule, which states that \((ab)^n = a^n \cdot b^n\).

\[
(-3x^4 y)^5 = (-3)^5 \cdot (x^4)^5 \cdot y^5
\]

Now, simplify each term:

1. \((-3)^5 = -243\)
2. \((x^4)^5 = x^{4 \cdot 5} = x^{20}\)
3. \(y^5 = y^5\)

Thus, the expression simplifies to:

\[
-243x^{20}y^5
\]

So, \((-3x^4 y)^5 = -243x^{20}y^5\).

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. Simplify \((2x^3 y^2)^4\).
2. Simplify \((5x^2 y^3 z)^3\).
3. Simplify \((7x^5 y^2)^2\).
4. What is \((-2x^4)^3\)?
5. Simplify \((4x^3 y z^2)^2\).

**Tip:** Remember, when raising a product to a power, distribute the exponent to each factor.

Simplify the expression (-3x^4 y)^5 by applying the power of a product rule. This detailed solution explains how to distribute the exponent across each term and arrive at the final simplified form -243x^{20}y^5. Ideal for students in Grades 9-10, covering exponent rules and algebraic manipulation.

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