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

Question

6620 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-18T13:59:15

#root(3)(4^4)#

#a^(color(red)n/color(green)m)=root(color(green)m)(a^color(red)n)#

So #4^(color(red)4/color(green)3)=root(color(green)3)(4^color(red)4)#

Answer 2 · 2017-04-18T13:59:40

See the entire solution process below:

First, we can use this rule of exponents to rewrite the expression:

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

#4^(4/3) = 4^(color(red)(4) xx color(blue)(1/3)) = (4^color(red)(4))^color(blue)(1/3) = 256^(1/3)#

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

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

#256^(1/color(red)(3)) = root(color(red)(3))(256)#