Question

Simplify the radical expression.

Answer 1

$\bf \sqrt[4]{625x^{12}y^8}~~ \begin{cases} 625=&5\cdot 5\cdot 5\cdot 5\\ &5^4\\ x^{12}=&x^{3\cdot 4}\\ &(x^3)^4\\ y^8=&y^{2\cdot 4}\\ &(y^2)^4 \end{cases}\implies \pm\sqrt[4]{5^4(x^3)^4(y^2)^4}\implies \begin{array}{llll} \pm5x^3y^2\\\\ 5|x^3|y^2\\\\ |5x^3y^2| \end{array}$