Find the value of #216^(-1/15)#?

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Answer 1 · 2017-06-07T13:34:57

#216^(-1/15)=1/root(5)6#

As #216=2xx2xx2xx3xx3xx3=2^3xx3^3#

#216^(-1/15)#

= #(2^3xx3^3)^(-1/15)#

= #(2^3)^(-1/15)xx(3^3)^(-1/15)#

= #2^((3xx(-1)/15))xx3^((3xx(-1)/15)#

= #2^(-1/5)xx3^(-1/5)#

= #1/2^(1/5)xx1/3^(1/5)#

= #1/6^(1/5)#

= #1/root(5)6#

Answer 2 · 2018-06-10T18:25:15

#1/(root(5)6)#

#(216)^(-1/15)#

#:.=(6^3)^(-1/15)#

#:.=6^(-3/15)#

#:.=6^(-1/5)#

#:.=1/(6^(1/5))#

#:.=1/(root(5)6)#