How do you simplify #\root[ 5] { 160x ^ { 12} y ^ { 15} }#?

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Answer 1 · 2017-12-05T03:01:19

See a solution process below:

First, rewrite the expression as:

#root(5)(32 * 5 * x^10 * x^2 * y^15) =>#

#root(5)(32x^10y^15 * 5x^2) =>#

#root(5)(2^5x^10y^15 * 5x^2)#

Now we can 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(5)(color(red)(2^5x^10y^15) * color(blue)( 5x^2)) =>#

#root(5)(color(red)(2^5x^10y^15)) * root(5)(color(blue)( 5x^2)) =>#

#2x^2y^3root(5)(color(blue)( 5x^2)) =>#