Let's simplify the expression \((4x)^3\).
We need to raise both the coefficient (which is 4) and the variable \(x\) to the third power. This can be done by applying the power to both the coefficient and the variable separately.
First, let's handle the coefficient:
[tex]\[ 4^3 \][/tex]
To raise 4 to the power of 3:
[tex]\[ 4^3 = 4 \times 4 \times 4 = 64 \][/tex]
Next, let's handle the variable:
[tex]\[ x^3 \][/tex]
Since raising \(x\) to the third power is simply:
[tex]\[ (x^1)^3 = x^{1 \cdot 3} = x^3 \][/tex]
Now, we combine the two results:
[tex]\[ (4x)^3 = 64 x^3 \][/tex]
So the simplified form of the expression \((4x)^3\) is:
[tex]\[ 64 x^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{64 x^3} \][/tex]
