Question

How do you write `root3(8^2)` as a fractional exponent?

Answer 1

See a solution process below:

Explanation:

First use this rule to eliminate the radical:

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

`root(color(red)(3))(8^2) => (8^2)^(1/color(red)(3))`

Now, use this rule to combine the exponents:

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

`(8^color(red)(2))^color(blue)(1/3) => 8^(color(red)(2) xx color(blue)(1/3)) => 8^(2/3)`