Answer :
We start by interpreting the expression as
[tex]$$
(4x^2)^3.
$$[/tex]
First, we note that when an entire product is raised to a power, we can apply the exponent to both factors:
[tex]$$
(4x^2)^3 = 4^3 \cdot (x^2)^3.
$$[/tex]
Next, we calculate each part separately:
1. For the coefficient:
[tex]$$
4^3 = 64.
$$[/tex]
2. For the variable part:
[tex]$$
(x^2)^3 = x^{2 \cdot 3} = x^6.
$$[/tex]
Combining these results gives:
[tex]$$
(4x^2)^3 = 64x^6.
$$[/tex]
Among the provided options, the expression that is equivalent to [tex]$64x^6$[/tex] is:
G. [tex]$\quad 64x^6$[/tex].
Thus, the correct answer is [tex]$\boxed{64x^6}$[/tex].
[tex]$$
(4x^2)^3.
$$[/tex]
First, we note that when an entire product is raised to a power, we can apply the exponent to both factors:
[tex]$$
(4x^2)^3 = 4^3 \cdot (x^2)^3.
$$[/tex]
Next, we calculate each part separately:
1. For the coefficient:
[tex]$$
4^3 = 64.
$$[/tex]
2. For the variable part:
[tex]$$
(x^2)^3 = x^{2 \cdot 3} = x^6.
$$[/tex]
Combining these results gives:
[tex]$$
(4x^2)^3 = 64x^6.
$$[/tex]
Among the provided options, the expression that is equivalent to [tex]$64x^6$[/tex] is:
G. [tex]$\quad 64x^6$[/tex].
Thus, the correct answer is [tex]$\boxed{64x^6}$[/tex].
