What is the cube root of x^8?

1 Answer
Oct 13, 2015

Answer:

#root(3)(x^8) = x^2 root(3)(x^2)#

or if you prefer:

#root(3)(x^8) = x^(8/3)#

Explanation:

For any #a, b in RR#, #root(3)(ab) = root(3)(a)root(3)(b)# and #root(3)(a^3) = a#

So:

#root(3)(x^8) = root(3)(x^6 * x^2) = root(3)((x^2)^3*x^2) = root(3)((x^2)^3)root(3)(x^2) = x^2 root(3)(x^2)#