Before leaving the valley, Eragon grabs his sword and belt from their hiding place in the forest. When Brom sees the sword he rubs his eyes thinking he is seeing things. When he realizes that the sword is real, he walks up to Eragon and inspects it. Having seen many Rider blades in his life, Brom instinctively can tell that while the sword is not made of metal, it was made with craftsmanship far beyond what Eragon should be capable of. The stone sword was obviously shaped with magic but the attention to detail and the uncut sapphire that is inside the handle and running up the side of the blade fascinates him to no end. Inspecting it further he notices that it is even enchanted.
"How did you make such a sword Eragon? I never even taught you how to enchant items yet."
Eragon looks at him with a raised eyebrow. "You mean it isn't supposed to be so easy to enchant items? What I enchanted it with was standard in my mind. I just made the blade drain energy from the gem instead of lowering its durability and added a simple size-altering enchantment that can make the tip of the blade extend over ten meters."
Brom has the most incredulous look on his face. "Standard? You call this standard? That is a high level enchantment you have made here. Even I would struggle to make such a sword. You're telling me you can do this with only a few weeks of training? You haven't even finished learning the ancient language yet!!! It was quite reckless of you to do this. Show me what your sword can do so I can determine how harsh I need to be with you in our next training session."
Eragon and Brom stop in a clearing in the forest. Eragon places Saphira off to the side and gives her some food before walking to the middle of the clearing with his sword.
"Afbrakka" (Enlarge). The sword blade lengthens by ten meters in the span of a second. "Brakka" (Reduce). The blade returns to its normal size in the same amount of time. Eragon starts to do simple sword movements whilst changing the size of the sword with a simple word, the blade humming through the air as he cuts through falling leaves. While his form is choppy and lacks grace he makes up for it in precision and the strength of his swings.
Brom's jaw hits the floor at the sight. He has never seen such an astounding feat of magic and sword skill from someone so young. Brom has fought in countless wars and seen true feats of magic but what Eragon just did with only a few weeks of training can easily qualify him as a high tier combatant of the human race. Such talent is unheard of even among the riders and puts him almost on par with the elves. And while his swordsmanship is not perfect, He has built himself a solid foundation from which Eragon should easily be able to incorporate other sword techniques with practice.
"What was Garrow feeding him?" Brom thinks to himself. "He has a decent swordsmanship foundation, his enchantment skills are at a high level, his muscles are well defined, and he can cast magic better than most human mages. My son is a genius greater than any I have ever seen. With the right training, he will be the best hope we have against Galbatorix. I'm happy with his progress but I can't condone reckless magic casting. Any one of his enchantments can kill him if he is not careful."
Brom rolls up his sleeves. "Now listen here son. I've told you this once and I will tell you again. Magic is dangerous. One wrong syllable and you will be a shriveled up corpse in a second. You will infer with me first before you do any more enchanting is that clear."
Eragon lowers his head. "Alright Brom. I will not enchant anything without your approval from now on. We can talk more about my magic on the road. We are due for a snow storm soon and I would like to get south of the valley before we get snowed in."
Eragon sheaths his sword and places Saphira on his shoulder. Her tail wraps around his neck as she cuddles up to him. They pick up their supplies and continue on their journey towards the town of Yazuac.
During their travels, Brom coaches Eragon in proper sword techniques along with some survival skills. The flora and fauna of this world, while mostly similar to his previous world, still has a few new ones that he has to familiarize himself with. Brom teaches him what mushrooms are poisonous, what plants are edible and how to cook them, the dangerous wildlife that they may encounter, and a multitude of other miscellaneous things that a normal sixteen year old would never be able to remember.
It's a good thing that he is not a normal sixteen year old. He is a reincarnator with the knowledge of his previous world and the excitement of getting to live in one of his favorite fantasy worlds. And from what Eragon has determined, he didn't just get thrown into this world without reincarnator bonus, or what most would call a "Golden Finger". For in his previous life he was never this clear headed and focused. This gives him the impression that he has received some kind of mind buff that will help him learn quicker and make him more efficient when casting magic. It also helps that when a human binds with a dragon, their magic capacity increases greatly over time. Then you factor in the ability to fill any gems he keeps on his person with excess energy every day, the power at his fingertips is already at a mid to high level for this world. The only thing that can make him exponentially stronger at this moment is for him to somehow get his hands on some Eldunari, a large crystal that is in the chest of every dragon that houses their mind and soul. Galbatorix has a host of these gems and has been slowly breaking the minds of the dragons trapped within over the past few decades.
"I just need to get the Eldunari from… from… Wait, what was I talking about again?" Eragon rubs the back of his head in contemplation before getting a smack in the back of the head by Brom.
"Think you can doze off in the middle of my lesson aye? Guess I will have to work you extra hard in our combat practice later. There will be many a time where you might not have a weapon nearby so we will start some unarmed combat training after supper."
Brom gives Eragon a devilish smirk as this was the first time he has caught him slacking and just couldn't resist giving him a taste of what his teachers used to do to him.