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

1 Answer
May 25, 2017

See a solution process below:

Explanation:

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)#