Question

How do you simplify `(\root[ 3] { 7p } ) ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the radical using this rule:

`root(color(red)(n))(x) = x^(1/color(red)(n))`

`(root(color(red)(3))(7p))^2 => ((7p)^(1/color(red)(3)))^2`

Now, we can use this rule of exponents to combine the inner and outer exponents:

`((7p)^color(red)(1/3))^color(blue)(2) => (7p)^(color(red)(1/3) xx color(blue)(2)) => (7p)^(2/3)`