Answer:
A. [tex]\frac{x^2\sqrt{x}}{3}[/tex]
Step-by-step explanation:
We have been given an expression [tex]\sqrt{\frac{2x^5}{18}}[/tex]. We are asked to find which expression is equivalent to our given expression.
Let me simplify our given expression. First of all we will divide 18 by 2 as:
[tex]\sqrt{\frac{2x^5}{2\cdot 9}}[/tex]
[tex]\sqrt{\frac{x^5}{9}}[/tex]
Now we will rewrite [tex]x^5 \text{ as } x^4\cdot x[/tex].
[tex]\sqrt{\frac{x^4\cdot x}{9}}[/tex]
Now we will write [tex]x^4\text{ and } 9[/tex] as perfect squares.
[tex]\sqrt{\frac{(x^2)^2\cdot x}{3^2}}[/tex]
Let us factor our perfect square from square-root.
[tex]\frac{x^2\sqrt{x}}{3}[/tex]
Therefore, option A is the correct choice.
