Question

How do you write the expression `2^(5/3)` in radical form?

Answer 1

See the solution process below:

Explanation:

First, we can rewrite this expression using this rule of exponents:

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

`2^(5/3) = 2^(color(red)(5) xx color(blue)(1/3)) = (2^color(red)(5))^color(blue)(1/3) = 32^(1/3)`

We can now use this rule of exponents and radicals to write this expression in radical form:

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

`32^(1/color(red)(3)) = root(color(red)(3))(32)`