How do you simplify #-4\root[ 3] { - 216x ^ { 2} y ^ { 3} }#?

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Answer 1 · 2017-11-14T15:10:51

See a solution process below:

First, rewrite the expression as:

#-4root(3)(216y^3 * -x^2) =>#

#-4root(3)((-8 * 27 * y^3) * x^2) =>#

#-4root(3)(-2^3 3^3y^3 * x^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))#

#-4root(3)(color(red)(-2^3 3^3y^3) * color(blue)(x^2)) =>#

#-4root(3)(color(red)(-2^3 3^3y^3)) * root(3)(color(blue)(x^2)) =>#

#-4(color(red)(-2 * 3 * y))root(3)(color(blue)(x^2)) =>#

#-4(color(red)(-6y))root(3)(color(blue)(x^2)) =>#

#24yroot(3)(color(blue)(x^2)) =>#