select the correct answer. which expression is equivalent to $7x^{2}sqrt{2x^{4}}cdot6sqrt{2x^{12}}$, if…

Explanation:

Step1: Multiply the coefficients

Multiply 7 and 6. $7\times6 = 42$.

Step2: Combine the square - root terms

Use the property $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$. So, $\sqrt{2x^{4}}\cdot\sqrt{2x^{12}}=\sqrt{2x^{4}\cdot2x^{12}}=\sqrt{4x^{16}}$. Since $\sqrt{4x^{16}} = 2x^{8}$ (because $\sqrt{4}=2$ and $\sqrt{x^{16}}=x^{8}$ for $x\neq0$).

Step3: Multiply with the $x^{2}$ term

Multiply $42$ and $x^{2}$ and $2x^{8}$. Using the rule $a^{m}\cdot a^{n}=a^{m + n}$, we have $42\times x^{2}\times2x^{8}=(42\times2)x^{2 + 8}=84x^{10}$.

Answer:

C. $84x^{10}$