How do you represent #5x^(4/9)# in radical form?

Question

834 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-06T03:43:17

See a solution process below:

First, we can write the expression as:

#5x^(4 xx 1/9)#

We can then use this rule of exponents to rewrite the #x# term:

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

#5x^(color(red)(4) xx color(blue)(1/9)) = 5(x^color(red)(4))^color(blue)(1/9)#

Now, we can use this rule of exponents and radicals to write the expression in radical form:

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

#5(x^4)^(1/color(red)(9)) = 5root(color(red)(9))(x^4)#