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

2 Answers
Aug 29, 2017

#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)#

Aug 29, 2017

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)#