What is the simplest form of ^4 sqrt 81x^8y^5

ANSWER[tex]3 {x}^{2} y \sqrt[4]{y} [/tex]EXPLANATIONWe want to simplify:[tex] \sqrt[4]{81 {x}^{8} {y}^{5} } [/tex]We can split the radical sign to obtain:[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} } [/tex]Or[tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y} [/tex][tex] \sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex][tex]\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y} [/tex]Recall that:[tex] \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } [/tex][tex]{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y} [/tex][tex]3 {x}^{2} y \sqrt[4]{y} [/tex]