Question

How do you simplify `2\root [ 3] { 16x ^ { 2} y ^ { 7} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression under the radical as:

`2root(3)8y^6 * 2x^2y)`

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))`

`2root(3)(color(red)(8y^6) * color(blue)(2x^2y)) =>`

`2root(3)(color(red)(8y^6)) * root(3)(color(blue)(2x^2y)) =>`

`2 * 2y^2 * root(3)(color(blue)(2x^2y)) =>`

`4y^2root(3)(color(blue)(2x^2y))`