To simplify the expression [tex]\(\left(7 x^3 y^3\right)^2\)[/tex], follow these steps:
1. Apply the power to the constant:
[tex]\[
(7)^2 = 49
\][/tex]
2. Apply the power to each variable separately using the power rule of exponents [tex]\((a^m)^n = a^{mn}\)[/tex]:
For [tex]\(x^3\)[/tex]:
[tex]\[
(x^3)^2 = x^{3 \cdot 2} = x^6
\][/tex]
For [tex]\(y^3\)[/tex]:
[tex]\[
(y^3)^2 = y^{3 \cdot 2} = y^6
\][/tex]
3. Combine all the parts:
[tex]\[
49 x^6 y^6
\][/tex]
Thus, the correct simplification of [tex]\(\left(7 x^3 y^3\right)^2\)[/tex] is:
[tex]\[
49 x^6 y^6
\][/tex]
Therefore, the answer is:
\[
49 x^6 y^6
\
