Answer:
[tex]3x^2y\sqrt[4]{y}[/tex]
Step-by-step explanation:
We have been given the radical expression [tex]\sqrt[4]{81x^8y^5}[/tex]
We can rewrite the terms inside the radical as:
[tex]81=3^4\\x^8=(x^2)^4\\y^5=y^4\cdot y[/tex]
Hence, the expression will become
[tex]\sqrt[4]{3^4\cdot(x^2)^4\cdot y^4\cdot y}[/tex]
Apply the exponent rule: [tex]\sqrt[n]{x^n}=x[/tex]
[tex]=3\cdotx^2\cdot y\sqrt[4]{y}\\\\=3x^2y\sqrt[4]{y}[/tex]
Hence, the simplified expression is [tex]3x^2y\sqrt[4]{y}[/tex]
