**Answer:** Cube root of 2.

We have 10^{1/10} vs 2^{1/3}.

Raise each to the power of 30 (since 10 x 3 = 30) to give:

10^{1/10 x 30} vs 2^{1/3 x 30}, which simplifies to:

10^{3} vs 2^{10}, which gives:

1000 vs 1024.

Therefore the cube root of 2 is larger. Alternatively we can use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.