Without,using mathematical, tables or calculator simplify
16^1\2 × 8^-4 × 3^-2/3 ÷ 81^2/3
16^1\2 = √16 = 4
8^-4 = 1/8^4 = 1/4096
3^-2/3 = 1/(3^2/3) = 1/(∛3^2) = 1/3^2 = 1/9
81^2/3 = ∛81^2 = ∛6561 = 9
Therefore, the expression simplifies to:
4 x 1/4096 x 1/9 ÷ 9
= 4/4096 x 1/9 ÷ 9
= 1/1024 x 1/9 ÷ 9
= 1/9216 ÷ 9
= 1/9216 x 1/9
= 1/82944
= 1/82944.