What is # 3^(3/2)# in radical form?

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Answer 1 · 2018-03-07T02:51:39

See a solution process below:

First, rewrite the expression as:

#3^(3 xx 1/2)#

Next, use this rule of exponents to rewrite the expression again:

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

#x^(color(red)(3) xx color(blue)(1/2)) => (x^color(red)(3))^color(blue)(1/2)#

Now, use this rule for exponents and radicals to write the expression in radical form:

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

Let #a = x^3#

#(x^3)^(1/color(red)(2)) => root(color(red)(2))(x^3) => sqrt(x^3)#