To find the expression equivalent to [tex]\((-4ab)^3\)[/tex], we need to expand and simplify the given expression step by step.
1. First, let's rewrite the expression [tex]\((-4ab)^3\)[/tex] using the properties of exponents.
2. According to the properties of exponents, [tex]\((xy)^n = x^n \cdot y^n\)[/tex]. Applying this to each part of the expression, we get:
[tex]\[
(-4ab)^3 = (-4)^3 \cdot (a)^3 \cdot (b)^3
\][/tex]
3. Next, calculate each term separately:
[tex]\[
(-4)^3 = -4 \cdot -4 \cdot -4 = -64
\][/tex]
[tex]\[
a^3 = a^3
\][/tex]
[tex]\[
b^3 = b^3
\][/tex]
4. Combining these results, we have:
[tex]\[
(-4)^3 \cdot a^3 \cdot b^3 = -64 \cdot a^3 \cdot b^3
\][/tex]
Therefore, the expression equivalent to [tex]\((-4ab)^3\)[/tex] is:
[tex]\[
-64a^3b^3
\][/tex]
Among the given options:
- [tex]\(-4a^3b^3\)[/tex]
- [tex]\(-12a^3b^3\)[/tex]
- [tex]\(-4ab^3\)[/tex]
- [tex]\(-64a^3b^3\)[/tex]
The correct option is [tex]\(-64a^3b^3\)[/tex].
