Question

Drag each tile to the correct box.

Answer 1

Answer:

$3x^{2}y^{2}\sqrt[4]{7xy^{3}}$.

Step-by-step explanation:

Since we have to find the simplified form of the expression as below

$\sqrt[4]{567x^{9}y^{11}}$

we will solve the expression as below

$=[567x^{9}y^{11}]^{\frac{1}{4}}$

$=(81\times 7)^{\frac{1}{4}}\times x^{\frac{9}{4}}\times y^{\frac{11}{4}}$

$=81^{\frac{1}{4}}.7^{\frac{1}{4}}.x^{\frac{8}{4}+\frac{1}{4}}.y^{\frac{8}{4}+\frac{3}{4}}$

$=(3^{4})^{\frac{1}{4}}.7^{\frac{1}{4}}.x^{2+\frac{1}{4}}.y^{2+\frac{3}{4}}$

$=3^{1}.7^{\frac{1}{4}}.x^{2}.x^{\frac{1}{4}}.y^{2}.y^{\frac{3}{4}}$

$=3.x^{2}.y^{2}.(7^{\frac{1}{4}}.x^{\frac{1}{4}}.y^{\frac{3}{4}})$

$=3x^{2}y^{2}.(7xy^{3})^{\frac{1}{4}}$

$=3x^{2}y^{2}\sqrt[4]{7xy^{3}}$.