Answer:
[tex]3x^{2}y^{2}\sqrt[4]{7xy^{3}}[/tex].
Step-by-step explanation:
Since we have to find the simplified form of the expression as below
[tex]\sqrt[4]{567x^{9}y^{11}}[/tex]
we will solve the expression as below
[tex]=[567x^{9}y^{11}]^{\frac{1}{4}}[/tex]
[tex]=(81\times 7)^{\frac{1}{4}}\times x^{\frac{9}{4}}\times y^{\frac{11}{4}}[/tex]
[tex]=81^{\frac{1}{4}}.7^{\frac{1}{4}}.x^{\frac{8}{4}+\frac{1}{4}}.y^{\frac{8}{4}+\frac{3}{4}}[/tex]
[tex]=(3^{4})^{\frac{1}{4}}.7^{\frac{1}{4}}.x^{2+\frac{1}{4}}.y^{2+\frac{3}{4}}[/tex]
[tex]=3^{1}.7^{\frac{1}{4}}.x^{2}.x^{\frac{1}{4}}.y^{2}.y^{\frac{3}{4}}[/tex]
[tex]=3.x^{2}.y^{2}.(7^{\frac{1}{4}}.x^{\frac{1}{4}}.y^{\frac{3}{4}})[/tex]
[tex]=3x^{2}y^{2}.(7xy^{3})^{\frac{1}{4}}[/tex]
[tex]=3x^{2}y^{2}\sqrt[4]{7xy^{3}}[/tex].
