Simplify the expression $\left(2x^{3}\right)^{4}$.

Apply the exponent rules $\left(xy\right)^{n} = x^{n} y^{n}$ and $\left(x^{a}\right)^{b} = x^{ab}$: $\left(2x^{3}\right)^{4} = 2^{4} \cdot \left(x^{3}\right)^{4} = 16 \cdot x^{12} = 16 x^{12}$. - Trap A forgets to raise $2$ to the $4$th power. - Trap B raises $2$ to $3$rd instead of $4$th. - Trap C adds exponents ($3 + 4$) instead of multiplying ($3 \times 4$). Load-bearing rules: $(ab)^{n} = a^{n}b^{n}$ and $(a^{p})^{q} = a^{pq}$. Both apply here.