How do you simplify #root3(1/7)#?
1 Answer
Explanation:
Since
According to the power of a quotient rule,
From here, we can say
We are left with
However, we cannot have a radical in the denominator. To rationalize this expression, we must try to make the denominator
#1/ 7^(1/3) * color(blue)(7^(2/3)/7^(2/3)) = 7^(2/3) / 7^(3/3) = 7^(2/3) /7 = root3 (7^2) /7 = root3 49 /7#
#1/ root 3 7 * color(blue)(root3 (7^2)/ root3 (7^2)) = root3 49 / root 3 343 = root 3 49/ 7#
So,