To determine the expression equivalent to [tex]\((-4abc)^3\)[/tex], we will use the properties of exponents and multiplication.
We start with the expression:
[tex]\[
(-4abc)^3
\][/tex]
Firstly, recognize that raising a product to a power means raising each factor in the product to that power. In this case, we have:
[tex]\[
(-4abc)^3 = (-4)^3 \cdot (a)^3 \cdot (b)^3 \cdot (c)^3
\][/tex]
Now let's handle each component separately:
1. Evaluate [tex]\((-4)^3\)[/tex]:
[tex]\[
(-4)^3 = -4 \times -4 \times -4
\][/tex]
[tex]\[
-4 \times -4 = 16
\][/tex]
[tex]\[
16 \times -4 = -64
\][/tex]
Thus, [tex]\((-4)^3 = -64\)[/tex].
2. Raise each variable to the power of 3:
[tex]\[
a^3, \quad b^3, \quad c^3
\][/tex]
So, combining all of these together, we get:
[tex]\[
(-4abc)^3 = (-4)^3 \cdot (a)^3 \cdot (b)^3 \cdot (c)^3 = -64a^3b^3c^3
\][/tex]
Therefore, the expression equivalent to [tex]\((-4abc)^3\)[/tex] is:
[tex]\[
-64a^3b^3c^3
\][/tex]
Among the given options, the correct answer is:
[tex]\[
-64a^3b^3c^3
\][/tex]
