Given expression is
[tex] \sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}[/tex]
Radical is fourth root
first we simplify the terms inside the radical
[tex]\frac{x^{11}}{x^7}=x^4[/tex]
[tex]\frac{y^(8)}{y^6}=y^2[/tex]
So the expression becomes
[tex] \sqrt[4]{\frac{16x^4y^2}{81}}[/tex]
Now we take fourth root
[tex]\sqrt[4]{16} = 2[/tex]
[tex]\sqrt[4]{81} = 3[/tex]
[tex]\sqrt[4]{x^4} = x[/tex]
We cannot simplify fourth root (y^2)
After simplification , expression becomes
[tex]\frac{2x\sqrt[4]{y^2}}{3}[/tex]
Answer is option B
