To determine the equivalent expression for [tex]\( (-6ab)^2 \)[/tex], let's break it down step by step.
1. Understand the Squaring Operation:
Squaring an expression means multiplying the expression by itself:
[tex]\[
(-6ab)^2 = (-6ab) \cdot (-6ab)
\][/tex]
2. Multiply the Constants:
First, multiply the numerical coefficients:
[tex]\[
-6 \times -6 = 36
\][/tex]
Notice that the product of two negative numbers is positive.
3. Multiply the Variables:
Next, consider the variables in the expression:
[tex]\[
a \times a = a^2 \quad \text{and} \quad b \times b = b^2
\][/tex]
4. Combine Everything Together:
Combine the results of the multiplication of the constants and the products of the variables:
[tex]\[
36 \cdot a^2 \cdot b^2 = 36a^2b^2
\][/tex]
Therefore, the expression [tex]\( (-6ab)^2 \)[/tex] simplifies to [tex]\( 36a^2b^2 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{36a^2b^2}
\][/tex]
So the correct option is:
B. [tex]\( 36a^2b^2 \)[/tex]
