To simplify the expression [tex]\(\left(7 x^3 y^3\right)^2\)[/tex], we can follow these steps:
1. Apply the power rule for coefficients:
When raising a coefficient to an exponent, we raise the number to that power.
[tex]\[
7^2 = 49
\][/tex]
2. Apply the power rule for each variable:
The power rule states that [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. We need to apply this for both [tex]\(x^3\)[/tex] and [tex]\(y^3\)[/tex].
For [tex]\(x\)[/tex]:
[tex]\[
(x^3)^2 = x^{3 \cdot 2} = x^6
\][/tex]
For [tex]\(y\)[/tex]:
[tex]\[
(y^3)^2 = y^{3 \cdot 2} = y^6
\][/tex]
3. Combine the simplified parts:
Now, combine the simplified coefficient and the variables:
[tex]\[
49 \cdot x^6 \cdot y^6
\][/tex]
Therefore, the correct simplification of [tex]\(\left(7 x^3 y^3\right)^2\)[/tex] is:
[tex]\[
\boxed{49 x^6 y^6}
\][/tex]
The correct answer from the given options is:
[tex]\[
49 x^6 y^6
\][/tex]
