select the correct answer. which expression is equivalent to $18x^{2}sqrt{14x^{8}}div6sqrt{7x^{4}}$, if…

Answer:

B. $3x^{4}\sqrt{2}$

Explanation:

Step1: Rewrite the division as a fraction

$\frac{18x^{2}\sqrt{14x^{8}}}{6\sqrt{7x^{4}}}$

Step2: Simplify the coefficient

$\frac{18}{6}=3$, so we have $3x^{2}\frac{\sqrt{14x^{8}}}{\sqrt{7x^{4}}}$

Step3: Use the quotient - rule of square roots $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

$3x^{2}\sqrt{\frac{14x^{8}}{7x^{4}}}$

Step4: Simplify the fraction inside the square root

$\frac{14x^{8}}{7x^{4}} = 2x^{4}$ (divide coefficients $14\div7 = 2$ and use $x^{m}\div x^{n}=x^{m - n}$, so $x^{8}\div x^{4}=x^{8 - 4}=x^{4}$)

Step5: Simplify the square root

$3x^{2}\sqrt{2x^{4}}=3x^{2}\cdot x^{2}\sqrt{2}=3x^{4}\sqrt{2}$