select the correct answer. which expression is equivalent to $4x^{2}sqrt{5x^{4}}cdot3sqrt{5x^{8}}$, if…

Answer:

A. $12x^{10}\sqrt{5}$

Explanation:

Step1: Multiply the coefficients

$4\times3 = 12$

Step2: Multiply the square - root parts

$\sqrt{5x^{4}}\times\sqrt{5x^{8}}=\sqrt{5\times5\times x^{4 + 8}}=\sqrt{25x^{12}}$ Since $\sqrt{25x^{12}} = 5x^{6}$ (because $\sqrt{25}=5$ and $\sqrt{x^{12}}=x^{6}$ for $x\neq0$)

Step3: Multiply the non - square - root $x$ part with the result

$x^{2}\times5x^{6}=5x^{2 + 6}=5x^{8}$

Step4: Combine with the coefficient

$12\times5x^{8}\sqrt{1}=12x^{10}\sqrt{5}$ (because $x^{2}\times x^{8}=x^{2 + 8}=x^{10}$)