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

Algebra

See full explanation below:

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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)##