To simplify the expression \((3x^4y)^3\), you can use the power of a product and the power of a power properties of exponents.
The expression can be simplified as follows:
\[ (3x^4y)^3 = 3^3 (x^4)^3 (y)^3 \]
Now compute each part:
- \(3^3 = 27\)
- \((x^4)^3 = x^{4 \cdot 3} = x^{12}\)
- \(y^3 = y^3\)
Combining all parts together gives:
\[ (3x^4y)^3 = 27x^{12}y^3 \]
So the simplified expression is:
\[ 27x^{12}y^3 \]