Question

Simplify the radical

Answer 1

I believe A should be the answer, hope that helps.

Answer 2

`\sqrt[4]{81x^(20)y^(24)}\\\\Use\ (a^n)^m=a^(nm)\\\\=\sqrt[4]{3^4x^(5\cdot4)y^(6\cdot4)}=\sqrt[4]{3^4(x^5)^4(y^6)^4}\\\\Use\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[4]{3^4}\cdot\sqrt[4]{(x^5)^4}\cdot\sqrt[4]{(y^6)^4}\\\\Use\ \sqrt[n]{a^n}=a\\\\=3|x^5|y^6\\\\Answer:\ \boxedy^6\\\\Why\ |x^5|?\ Beacause\ \sqrt[4]{x^(20)}\geq0\to x^5\geq0\ if\ x\geq0\ and\ x^5<0\ if\ x<0.`