The Solution:
The given expression is
[tex]\sqrt[]{18x^4y^5}[/tex][tex]\begin{gathered} \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3)(3)(x)(x)(x)(x)(y)(y)(y)(y)(y)} \\ \\ \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3^2)(x^2)(x^2)(y^2)(y^2)(y)}=3x^2y^2\text{ }\sqrt[]{2y} \end{gathered}[/tex]
Clearly, we have that Ayna's work was wrong.
[tex]\begin{gathered} \text{ Ayna wrote} \\ 2x^2y^2\sqrt[]{3x^2y}\text{ instead of} \\ \\ 3x^2y^2\sqrt[]{2y} \end{gathered}[/tex]
But Lesile' work is correct.
Thus, the correct answer is
[tex]3x^2y^2\text{ }\sqrt[]{2y}[/tex]
