# 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,