To solve the expression [tex]\((-4abc)^3\)[/tex], we need to simplify it step by step:
1. Understand the structure of the expression:
The expression is in the form [tex]\((x)^3\)[/tex], where [tex]\(x = -4abc\)[/tex].
2. Apply the power to each component within the parentheses:
[tex]\[
(-4abc)^3 = (-4)^3 \cdot (a)^3 \cdot (b)^3 \cdot (c)^3
\][/tex]
3. Calculate each part separately:
- Calculate [tex]\((-4)^3\)[/tex]:
[tex]\[
(-4)^3 = (-4) \times (-4) \times (-4) = -64
\][/tex]
- Calculate [tex]\((a)^3\)[/tex]:
[tex]\[
(a)^3 = a^3
\][/tex]
- Calculate [tex]\((b)^3\)[/tex]:
[tex]\[
(b)^3 = b^3
\][/tex]
- Calculate [tex]\((c)^3\)[/tex]:
[tex]\[
(c)^3 = c^3
\][/tex]
4. Combine all the results:
[tex]\[
(-4abc)^3 = -64 \cdot a^3 \cdot b^3 \cdot c^3
\][/tex]
So, the expression [tex]\((-4abc)^3\)[/tex] simplifies to [tex]\(-64a^3b^3c^3\)[/tex].
Given the choices:
1. [tex]\(-64a^3b^3c^3\)[/tex]
2. [tex]\(-12a^3b^3c^3\)[/tex]
3. 12a^3bc
4. [tex]\(64a^8b^8c^3\)[/tex]
The correct answer is:
[tex]\[ \boxed{-64a^3b^3c^3} \][/tex]
