By default: No effect
As stated by Oblivious Sage, Dragon Breath is not normally an Arcane power. The power you described only affects Arcane powers, and thus would have no effect on Dragon Breath.
However, the feat Ancient Soul can turn Dragon Breath into an Arcane power, so let's assume you take that.
With Ancient Soul: Still no effect
The item's power is described as increasing the range of an attack power used with it. However, a Close power doesn't have a range. It has a size, indicated by the number at the end, which is distinct from a range, as Area powers have both size and range. Therefore, the utility power would normally have no effect on Dragon Breath.
However, the feat Hurl Breath can turn Dragon Breath into (if I recall the numbers correctly) an Area Burst 2 Within 10. If we assume you also take that feat, we can finally see some effects.
With both Ancient Soul and Hurl Breath: Increases how far away you can place the burst when used as an Area power
Hurl Breath gives you the option to use Dragon Breath as an Area Burst 2 Within 10. An Area power has both a size (how big the area of effect is) and a range (how far away you can place the origin square of the effect), with the first number being the size and the second being the range. As the utility power described increases the range of the power, that is what would be affected.
Therefore, assuming a +3 enhancement bonus on your implement, as well as the two necessary feats, the utility power would allow you to upgrade Dragon Breath into an Area Burst 2 Within 13, but would still have no effect if Dragon Breath is used as a Close Blast.