How do you write $root3(8^2)$ as a fractional exponent?

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Answer 1 · 2017-05-25T00:07:18

See a solution process below:

First use this rule to eliminate the radical:

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

$root(color(red)(3))(8^2) => (8^2)^(1/color(red)(3))$

Now, use this rule to combine the exponents:

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

$(8^color(red)(2))^color(blue)(1/3) => 8^(color(red)(2) xx color(blue)(1/3)) => 8^(2/3)$

How do you write root3(8^2)root3(8^2) as a fractional exponent?