Answer:
FIRST OPTION.
Step-by-step explanation:
Given the expression [tex]\sqrt{\frac{2x^5}{18}}[/tex], you can find an equivalent expression simplifying.
The first step is to descompose 18 into its prime factors:
[tex]18=2*3*3=2*3^2[/tex]
Remember the Product of powers property, which states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then you can rewrite the expression in this form:
[tex]\sqrt{\frac{2x^4x}{2*3^2}[/tex]
Knowing that [tex]\sqrt[n]{a^n}=a[/tex], you get the following equivalent expression:
[tex]\sqrt{\frac{2x^4x}{2*3^2}[/tex]
[tex]\frac{x^2}{3}\sqrt{\frac{2x}{2}}[/tex]
[tex]\frac{x^2\sqrt{x}}{3}[/tex]
