which expression is equivalent to $sqrt{\frac{8}{x^{6}}}$? assume $x > 0$.\n$\frac{x^{3}sqrt{2}}{2}$\n$\frac{…

which expression is equivalent to $sqrt{\frac{8}{x^{6}}}$? assume $x > 0$.\n$\frac{x^{3}sqrt{2}}{2}$\n$\frac{4sqrt{2}}{x^{3}}$\n$\frac{sqrt{2}}{2x^{3}}$\n$\frac{2sqrt{2}}{x^{3}}$

which expression is equivalent to $sqrt{\frac{8}{x^{6}}}$? assume $x > 0$.\n$\frac{x^{3}sqrt{2}}{2}$\n$\frac{4sqrt{2}}{x^{3}}$\n$\frac{sqrt{2}}{2x^{3}}$\n$\frac{2sqrt{2}}{x^{3}}$

Answer

Answer:

D. $\frac{2\sqrt{2}}{x^{3}}$

Explanation:

Step1: Simplify the numerator

$\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$

Step2: Simplify the denominator

$\sqrt{x^{6}} = x^{3}$ (since $\sqrt{a^{n}}=a^{\frac{n}{2}}$ and here $n = 6$, so $\sqrt{x^{6}}=x^{\frac{6}{2}}=x^{3}$)

Step3: Combine the simplified numerator and denominator

$\sqrt{\frac{8}{x^{6}}}=\frac{\sqrt{8}}{\sqrt{x^{6}}}=\frac{2\sqrt{2}}{x^{3}}$