To determine the expression equivalent to \(\left(2 x^4 y\right)^3\), follow these steps:
1. Identify the components involved in the expression:
- The base numerical coefficient is \(2\).
- The variable \(x\) is raised to the power of 4: \(x^4\).
- The variable \(y\) is raised to the power of 1: \(y\).
2. Apply the exponent to each component:
- For the numerical coefficient \(2\): \((2)^3\).
- For the variable \(x\) raised to the power of 4: \((x^4)^3\).
- For the variable \(y\) raised to the power of 1: \((y)^3\).
3. Calculate each component separately:
- For the numerical coefficient: \((2)^3 = 2 \times 2 \times 2 = 8\).
- For the variable \(x\) with exponents multiplied: \((x^4)^3 = x^{4 \times 3} = x^{12}\).
- For the variable \(y\) with exponents multiplied: \((y)^3 = y^{1 \times 3} = y^3\).
4. Combine the results to form the simplified expression:
- Combining the calculated components, we get: \(8 x^{12} y^3\).
Thus, the expression equivalent to [tex]\(\left(2 x^4 y\right)^3\)[/tex] is [tex]\(\boxed{8 x^{12} y^3}\)[/tex].
