Question

How do you simplify `192^(1/6)`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the expression as:

`(64 * 3)^(1/6) => (2^6 * 3)^(1/6) => (2^6)^(1/6) * 3^(1/6)`

We can use these rules of exponents to simplify the `2"'s"` term:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))` and `a^color(red)(1) = a`

`(2^color(red)(6))^color(blue)(1/6) * 3^(1/6) => 2^(color(red)(6)xxcolor(blue)(1/6)) * 3^(1/6) => 2^color(red)(1) * 3^(1/6) => 2 * 3^(1/6)`

If necessary, we can write this in radical form using this rule for exponents:

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

`2 * 3^(1/color(red)(6)) = 2root(color(red)(6))(3)`