Question

How do you write the expression `2^(1/6)` in radical form?

Answer 1

`root(6)2`

Explanation:

When we're looking at an exponent that is a fraction, the top number is the "Nth" power (squared, cubed, etc) and the bottom number is the Nth root (square root, cube root, etc).

Our question has a 1 as the numerator, and so no special power. The denominator is a 6, so it's the 6th root. We write that as:

`root(6)2`

Answer 2

`root(6)(2)`

Explanation:

`color(blue)(2^(1/6)`

To convert it into the radical form, we use this

`color(brown)(x)^(color(orange)(y)/color(violet)(z))=(root(color(violet)(z))(x))^color(orange)(y)`

Then,

`:.color(brown)(2)^(color(orange)(1)/color(violet)(6))=(root(color(violet)(6))(2))^color(orange)(1)`

`=color(blue)(root(6)(2)`

Hope this answer helps!..