\sqrt[6]{((2)/(3))^(2) } as a power

Question

`\sqrt[6]{((2)/(3))^(2) }` as a power

Answer 1

`(2)/(3)^{(1)/(3)}`

Explanation:

The n-th root is the same thing as the denominator of an exponent.

For example.
`\sqrt[3]{x} = x^{(1)/(3)}`

and
`\sqrt[4]{x} = x^{(1)/(4)}`

and
`√(x) = x^{(1)/(2)}`

So

`\sqrt[6]{(2)/(3)^(2)} = (2)/(3)^{(2)((1)/(6))} = (2)/(3)^{(2)/(6)} = (2)/(3)^{(1)/(3)}`