Question 1 of 5

Select the correct answer.

Which expression is equivalent to the given expression?
[tex](-4abc)^3[/tex]

A. [tex]-64a^3b^3c^3[/tex]
B. [tex]-12a^3b^3c^3[/tex]
C. [tex]12a^3bc[/tex]
D. [tex]64a^8b^8c^3[/tex]



Answer :

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]