How do you simplify #\root[ 6] { 128n ^ { 8} }#?

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Answer 1 · 2017-11-13T14:36:28

See a solution process below:

First, rewrite the expression as:

#root(6)(64n^6 * 2n^2)#

Now, use this rule for radicals to simplify the expression:

#root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))#

#root(6)(color(red)(64^n^6) * color(blue)(2n^2)) =>#

#root(6)(color(red)(64n^6)) * root(6)(color(blue)(2n^2)) =>#

#root(6)(color(red)(2^6n^6)) * root(6)(color(blue)(2n^2)) =>#

#color(red)(2n)root(6)(color(blue)(2n^2))#