Question

How do you rationalize the denominator and simplify `1/root3(x^2)`?

Answer 1

`1/root(3)(x^2)=color(red)(x^(-4/3))`

Explanation:

`1/root(3)(x^2)`
`color(white)("XXX")=1/root(3)(x^2)xxroot(3)(x^2)/root(3)(x^2)xxroot(3)(x^2)/root(3)(x^2)`

`color(white)("XXX")=((root(3)(x^2))^2)/(x^2)`

`color(white)("XXX")=(x^(1/3))^2xx`1/(x^2)`

`color(white)("XXX")=x^(2/3) xx x^(-2)`

`color(white)("XXX")=x^((2/3-2))`

`color(white)("XXX")=x^((-4/3))`

Answer 2

See a solution process below:

Explanation:

To rationalize the denominator we must multiply the fraction by the appropriate value of `1`:

`root(3)(x)/root(3)(x) xx 1/root(3)(x^2) =>`

`(root(3)(x) xx 1)/(root(3)(x) xx root(3)(x^2)) =>`

`root(3)(x)/(root(3)(x xx x^2)) =>`

`root(3)(x)/(root(3)(x^3)) =>`

`root(3)(x)/x`