which expression is equivalent to $(4y^{2})^{3}(3y^{2})$?\n$12y^{8}$\n$12y^{12}$\n$192y^{8}$\n$192y^{12}$

Explanation:

Step1: Expand ((4y^{2})^{3})

Utilizar la regla ((ab)^n=a^n b^n) y ((a^m)^n=a^{mn}). Entonces ((4y^{2})^{3}=4^{3}(y^{2})^{3}=64y^{6}).

Step2: Multiplicar por (3y^{2})

Multiplicar (64y^{6}) por (3y^{2}). Usar la regla (a^m\times a^n=a^{m + n}), entonces (64y^{6}\times3y^{2}=(64\times3)y^{6 + 2}=192y^{8}).

Answer:

C. (192y^{8})