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

2 Answers

#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#

Oct 16, 2016

#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!..