How do you write #21^(9/4)# in radical notation?

Question

2467 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-07T21:26:26

#root(4)21^9#

or

#441root(4)21#

Since #a^(m/n)=root(n)a^m#

you get:

#21^(9/4)=root(4)21^9#

or

#21^2root(4)21=441root(4)21#

Answer 2 · 2017-01-07T21:26:54

See full explanation below:

We can use the following rule for exponents to rewrite this expression:

#x^(color(red)(a)/color(blue)(b)) = (x^color(red)(a))^(1/color(blue)(b))#

#21^(9/4) -> (21^9)^(1/4)#

The next rule for exponents we need to employ to get this into radical notation is:

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

#(21^9)^(1/color(red)(4)) ->#

#root(color(red)(4))(21^9)#