The expression that is equivalent to [tex]\sqrt{\frac{2x^{5} }{18} }[/tex] is [tex]x^{2} \frac{\sqrt{x} }{3}[/tex].
The given expression is [tex]\sqrt{\frac{2x^{5} }{18} }[/tex].
We can write the above expression as [tex]\sqrt{\frac{2.x^{2} .x^{2} .x}{2*9} }[/tex]
The square root of [tex]x^{2}[/tex] i.e. [tex]\sqrt{x^{2} } =x[/tex] and same for [tex]\sqrt{9} =3[/tex].
So, we can write the expression [tex]\sqrt{\frac{2.x^{2} .x^{2} .x}{2*9} }[/tex] as [tex]\frac{x.x\sqrt{x} }{3}[/tex].
So, [tex]\frac{x.x\sqrt{x} }{3}= x^{2} \frac{\sqrt{x} }{3}[/tex].
Therefore, the expression that is equivalent to [tex]\sqrt{\frac{2x^{5} }{18} }[/tex] is [tex]x^{2} \frac{\sqrt{x} }{3}[/tex].
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