2 / [81^(1/6)]

= 2 / [(3^4)^(1/6)]

= 2 / [3^(4/6)]

= 2 / [3^(2/3)]

Now rationalize the denominator,

Multiply both numerator and denominatoe by 3^(1/3),

= [2 *3^(1/3)] / [3^(2/3) *3^(1/3)]

= [2 *3^(1/3)] / [3^(2/3 +1/3)]

= [2 *3^(1/3)] / [3^(3/3)]

= [2 *3^(1/3)] / [3^(1)]

= [2 *3^(1/3)] / 3 ------------answer

or,

= (2/3)*3^(1/3) ---------answer