How do you simplify #\root [ 3] { 16x ^ { 5} y ^ { 9} z ^ { 10} }#?

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Answer 1 · 2018-05-29T21:36:50

See a solution process below:

First, rewrite the expression under the radical as:

#root(3)(8x^3y^9z^9 * 2x^2z)#

Next, 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(3)(color(red)(8x^3y^9z^9) * color(blue)(2x^2z)) =>#

#root(3)(color(red)(8x^3y^9z^9)) * root(3)(color(blue)(2x^2z)) =>#

#2xy^3z^3 * root(3)(color(blue)(2x^2z)) =>#

#2xy^3z^3root(3)(color(blue)(2x^2z))#