Solution:
1. [tex]\frac{2 \times ({2 x y^3})^\frac{1}{6}}{xy^2}[/tex]
[tex]=2^{1+\frac{1}{6}}\times[/tex][tex]\frac{1}{x^(1-\frac{1}{6})}\times y^{2-\frac{3}{6}}[/tex]
[tex]=2^{\frac{7}{6}} \times \frac{1}{x^{\frac{5}{6}}\times y^\frac{3}{2}}}[/tex]→→(C)
2. [tex]\frac{(27 x y^3)^{\frac{1}{4}}}{3 xy^2}=\frac{1}{3^{1-\frac{3}{4}}}\times\frac{1}{ x^{1-\frac{1}{4}} }\times \frac{1}{ y^{2-\frac{3}{4}}}=\frac{1}{3^{\frac{3}{4}}x^\frac{3}{4}y^\frac{5}{4}}=\frac{1}{({3^3x^3y^5})^{\frac{1}{4}}}[/tex]→→→(B)
[tex]3. \frac{(3 x y^3)^{\frac{1}{4}}}{x^3\times y^4}\\\\=\frac{3^\frac{1}{4}}{x^{3-\frac{1}{4}}y^{4-\frac{3}{4}}}\\\\ \frac{3^\frac{1}{4}}{(x^{11}y^{13})^\frac{1}{4}}[/tex]→→(A)
[tex]4. \frac{(32 x^5y)^\frac{1}{6}}{x^2y}=\frac{2^\frac{5}{6}}{x^{2-\frac{5}{6}}y^{1-\frac{1}{6}}}\\\\ \frac{2^\frac{5}{6}}{x^{\frac{7}{6}}y^{\frac{5}{6}}}\\\\ (\frac{2^5}{x^7y^5})^\frac{1}{6}[/tex]→→(D)
