Answer :
To determine which expression is equivalent to [tex]\((4x^2)^3\)[/tex], follow these steps:
1. Identify the components of the expression:
- You have [tex]\((4x^2)^3\)[/tex], which means both the number [tex]\(4\)[/tex] and the variable [tex]\(x^2\)[/tex] are being raised to the power of [tex]\(3\)[/tex].
2. Apply the power of a power property:
- For the number [tex]\(4\)[/tex], calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
- For the variable part [tex]\(x^2\)[/tex], apply the power of a power rule [tex]\((x^a)^b = x^{a \cdot b}\)[/tex]:
[tex]\[
(x^2)^3 = x^{2 \cdot 3} = x^6
\][/tex]
3. Combine the results:
- The expression [tex]\((4x^2)^3\)[/tex] simplifies to:
[tex]\[
64x^6
\][/tex]
Therefore, the equivalent expression is [tex]\(\boxed{64x^6}\)[/tex], which corresponds to the second option in the list.
1. Identify the components of the expression:
- You have [tex]\((4x^2)^3\)[/tex], which means both the number [tex]\(4\)[/tex] and the variable [tex]\(x^2\)[/tex] are being raised to the power of [tex]\(3\)[/tex].
2. Apply the power of a power property:
- For the number [tex]\(4\)[/tex], calculate [tex]\(4^3\)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
- For the variable part [tex]\(x^2\)[/tex], apply the power of a power rule [tex]\((x^a)^b = x^{a \cdot b}\)[/tex]:
[tex]\[
(x^2)^3 = x^{2 \cdot 3} = x^6
\][/tex]
3. Combine the results:
- The expression [tex]\((4x^2)^3\)[/tex] simplifies to:
[tex]\[
64x^6
\][/tex]
Therefore, the equivalent expression is [tex]\(\boxed{64x^6}\)[/tex], which corresponds to the second option in the list.
