Question

How do you write `4^(4/3)` in radical form?

Answer 1

`root(3)(4^4)`

Explanation:

`"Fractional exponents are expressed in radical form using"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^(m/n)=root(n)(a^m))color(white)(2/2)|)))`

`rArr4^(4/3)=root(3)(4^4)`

Answer 2

See a solution process below

Explanation:

First, rewrite the expression as:

`4^(4 * 1/3)`

Use this rule to rewrite the expression again:

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

`4^(color(red)(4) xx color(blue)(1/3)) = (4^color(red)(4))^color(blue)(1/3)`

When can then use this rule to rewrite the expression in radical form:

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

`(4^4)x^(1/color(red)(3)) = root(color(red)(3))(4^4)`

If necessary, we can simplify the term within the radical as:

`root(3)(4^4) = root(3)(256)`

Also, if necessary, we can simply the term within the radical using this rule:

`root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))`

`root(3)(4^4) = root(3)(color(red)(4^3) * color(blue)(4)) = root(3)(color(red)(4^3)) * root(3)(color(blue)(4)) = 4root(3)(4)`