To simplify the expression [tex]\(\left( -6ba^3 \right)^2\)[/tex], we will follow these steps:
1. Square the Coefficient:
[tex]\[
(-6)^2 = 36
\][/tex]
Squaring [tex]\(-6\)[/tex] results in positive 36.
2. Square the Variables:
Each variable inside the parentheses is squared according to the exponentiation rule [tex]\((x^m)^n = x^{m \cdot n}\)[/tex].
- For [tex]\(b\)[/tex]:
[tex]\[
(b)^2 = b^2
\][/tex]
- For [tex]\(a^3\)[/tex]:
[tex]\[
(a^3)^2 = a^{3 \cdot 2} = a^6
\][/tex]
3. Combine Them:
We combine the squared coefficient and the squared variables into a single expression.
[tex]\[
36 \cdot b^2 \cdot a^6
\][/tex]
Thus, the simplified form of the expression [tex]\(\left( -6ba^3 \right)^2\)[/tex] is:
[tex]\[
36b^2a^6
\][/tex]
