How do you simplify #\frac { 20\root[ 4] { 128n ^ { 6} } } { - 2\root [ 4] { 4n } }#?

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Answer 1 · 2017-07-22T02:13:58

See a solution process below:

First, simplify the constants:

#(20root(4)(128n^6))/(-2root(4)(4n)) =>#

#(-10root(4)(128n^6))/root(4)(4n)#

Next rewrite and simplify the radical in the numerator as:

#(-10root(4)(16n^4 * 8n^2))/root(4)(4n) =>#

#(-10root(4)(16n^4)root(4)(8n^2))/root(4)(4n) =>#

#(-10 * 2nroot(4)(8n^2))/root(n)(4n) =>#

#(-20nroot(4)(8n^2))/root(n)(4n)#

Next, combine the radicals as:

#-20nroot(4)((8n^2)/(4n)) =>#

#-20nroot(4)(2n)#