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

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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:

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

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

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

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