To determine the expression equivalent to [tex]\((-6ab)^2\)[/tex], we will follow these steps:
1. Simplify the expression inside the parentheses:
We have [tex]\(-6ab\)[/tex] inside the parentheses.
2. Square the entire expression:
We need to square each component inside the parentheses, based on the properties of exponents. Let's expand the expression as follows:
[tex]\[
(-6ab)^2 = (-6)^2 \cdot (a)^2 \cdot (b)^2
\][/tex]
3. Calculate the square of each factor:
- Squaring [tex]\(-6\)[/tex], we get:
[tex]\[
(-6)^2 = 36
\][/tex]
- Squaring [tex]\(a\)[/tex], we get:
[tex]\[
(a)^2 = a^2
\][/tex]
- Squaring [tex]\(b\)[/tex], we get:
[tex]\[
(b)^2 = b^2
\][/tex]
4. Combine the results:
Now, multiply these squared terms together:
[tex]\[
36 \cdot a^2 \cdot b^2
\][/tex]
Hence, the resulting expression is:
[tex]\[
36 a^2 b^2
\][/tex]
So, the correct answer is:
B. [tex]\(36 a^2 b^2\)[/tex]
