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

$\sqrt[6]{2}$

#### 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:

$\sqrt[6]{2}$

Oct 16, 2016

$\sqrt[6]{2}$

#### Explanation:

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

To convert it into the radical form, we use this

${\textcolor{b r o w n}{x}}^{\frac{\textcolor{\mathmr{and} a n \ge}{y}}{\textcolor{v i o \le t}{z}}} = {\left(\sqrt[\textcolor{v i o \le t}{z}]{x}\right)}^{\textcolor{\mathmr{and} a n \ge}{y}}$

Then,

$\therefore {\textcolor{b r o w n}{2}}^{\frac{\textcolor{\mathmr{and} a n \ge}{1}}{\textcolor{v i o \le t}{6}}} = {\left(\sqrt[\textcolor{v i o \le t}{6}]{2}\right)}^{\textcolor{\mathmr{and} a n \ge}{1}}$

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