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#