How do you write #y^(5/4)# in radical form?

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Answer 1 · 2018-03-11T22:45:40

#y^(5/4) = root4(y^5)#

#y^(x/n) = rootn(y^x)#

#y^(5/4) = root4(y^5)#

Answer 2 · 2018-03-11T22:48:49

See a solution process below:

First, rewrite the exponent as:

#y^(5 * 1/4)#

Then use this rule of exponents to rewrite the expression:

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

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

Then use this rule of exponents and radicals to write the expression in radical form:

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

If you want to simplify this expression we can use this rule for radicals:

#root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))#

#root(4)(y^5) => root(4)(color(red)(y^4) * color(blue)(y)) = root(4)(color(red)(y^4)) * root(4)(color(blue)(y)) => yroot(4)(y)#