How do you simplify #192^(1/6)#?

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Answer 1 · 2017-08-13T21:41:49

See a solution process below:

First, we can rewrite the expression as:

#(64 * 3)^(1/6) => (2^6 * 3)^(1/6) => (2^6)^(1/6) * 3^(1/6)#

We can use these rules of exponents to simplify the #2"'s"# term:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))# and #a^color(red)(1) = a#

#(2^color(red)(6))^color(blue)(1/6) * 3^(1/6) => 2^(color(red)(6)xxcolor(blue)(1/6)) * 3^(1/6) => 2^color(red)(1) * 3^(1/6) => 2 * 3^(1/6)#

If necessary, we can write this in radical form using this rule for exponents:

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

#2 * 3^(1/color(red)(6)) = 2root(color(red)(6))(3)#