What is the equivalent radical expression for the exponential expression below? 18^1/2

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Answer 1 · 2018-07-25T21:32:29

See a solution process below:

Use this rule to change the term to a radical:

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

#18^(1/color(red)(2)) => root(color(red)(2))(18) => sqrt(18)#

We can simplify this expression, if necessary, by using this rule for radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(18) => sqrt(color(red)(9) * color(blue)(2)) => sqrt(color(red)(9)) * sqrt(color(blue)(2)) => 3sqrt(2)#

Answer 2 · 2018-07-25T21:33:35

See below

#a^(m/n)= rootn(a^m)#

#18^(1/2)= sqrt18= sqrt(9*2)= 3sqrt2#