Question

Simplify the expression 4√−16⁢𝑥^16⁢𝑦^8 with positive rational exponents. Order the variables alphabetically.

Answer 1

Interpret the 4th root as a 1/4 power:
(−16 x^16 y^8)^{1/4} = (−1)^{1/4}·16^{1/4}·x^{16/4}·y^{8/4}
= (−1)^{1/4}·2·x^4·y^2.

With variables in alphabetical order:
2 x^4 y^2 (−1)^{1/4}.

(If you want the principal complex value, (−1)^{1/4} = e^{iπ/4} = (1+i)/√2, so the principal 4th root is √2(1+i) x^4 y^2.)