To determine which expression is equivalent to [tex]\(\left(2 x^4 y\right)^3\)[/tex], we need to carefully apply the rules of exponents.
First, let's expand the given expression [tex]\(\left(2 x^4 y\right)^3\)[/tex]:
1. Expand each component inside the parentheses raised to the power of 3:
[tex]\[
(2 x^4 y)^3
\][/tex]
2. Apply the power of 3 to each individual term inside the parentheses:
[tex]\[
(2)^3 \cdot (x^4)^3 \cdot (y)^3
\][/tex]
3. Calculate each exponent:
[tex]\[
2^3 \cdot (x^4)^3 \cdot y^3
\][/tex]
- [tex]\(2^3 = 8\)[/tex]
- [tex]\((x^4)^3 = x^{4 \cdot 3} = x^{12}\)[/tex]
- [tex]\(y^3 = y^3\)[/tex]
4. Combine all the components:
[tex]\[
8 \cdot x^{12} \cdot y^3
\][/tex]
Thus, the fully expanded expression is:
[tex]\[
8 x^{12} y^3
\][/tex]
So, the expression equivalent to [tex]\(\left(2 x^4 y\right)^3\)[/tex] is:
[tex]\(\boxed{8 x^{12} y^3}\)[/tex]
