Question

Simplify 4√16⁢(𝑥−3)^12.

Answer 1

Interpret the expression as the fourth root of [16(x−3)^12].

16 = 2^4 and (x−3)^12 = ((x−3)^4)^3, so
fourth root = 2·|x−3|^3.

(If x ≥ 3 you can drop the absolute value and get 2(x−3)^3.)