How do you simplify $root4(16/81)$ ?

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Answer 1 · 2018-07-15T21:19:45

$2/3$

Note that $(2/3)^4=16/81$

Answer 2 · 2018-07-15T21:26:36

$2/3$

$root(4)(16/81)=root(4)(16)/root(4)(81)=2/3$

Answer 3 · 2018-07-16T02:36:18

$color(purple)(=> 2/3$

$root 4 (16/81)$

$(a ^m)^n = a^(mn)$

$=> root 4 ((2 * 2 * 2 * 2) / (3 * 3 * 3 * 3))$

$=> root 4 (2^4 / 3^4)$

$=> (2^4 / 4^4)^(1/4)$

$=> (2^(4/4)/ 3^(4/4))$

$color(purple)(=> 2/3$

How do you simplify root4(16/81)root4(16/81)?