Question

(-6xy^4)^3

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, we can apply this to \((-6xy^4)^3\) as follows:
\((-6xy^4)^3 = (-6)^3 \cdot x^3 \cdot (y^4)^3\)

Step2: Calculate each term

First, calculate \((-6)^3\). We know that \((-6)^3 = -6 \times -6 \times -6 = -216\).
Next, for \((y^4)^3\), we use the power of a power rule \((a^m)^n = a^{mn}\), so \((y^4)^3 = y^{4 \times 3} = y^{12}\).
And \(x^3\) remains as it is.
Now, multiply all these terms together: \(-216 \cdot x^3 \cdot y^{12} = -216x^3y^{12}\)

Answer:

\(-216x^3y^{12}\)