

I haven't watched Dragon Ball in detail, but I think something like this has
never been explained and it doesn't make sense to me at all.

It took all Dragon Ball for Goku to go from power level of 10 to a maximum of
950 in his fight against Raditz. However, in much less time than what took
Dragon Ball to happen, he managed to get to 8000 in base form to fight Vegeta
in relatively little time, and then to 300000 in base form in even less time
to fight against Freezer, and so on...

It's obvious that if you get better training methods, you can improve faster.
However, I think something like that doesn't make sense in this case even for
an anime. I'd like to know if there's an in-universe explanation for this
exponential growth in power level.


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dragon-ball
Is there an explanation to the "exponential" growth of power levels in Z fighters?


One possible answer is that Saiyans get way more powerful than before if they
agonize (and survive). It's called
[Zenkai](http://dragonball.wikia.com/wiki/Zenkai). This ability is found in
pure Saiyan, half-blood and even Cell.

One example is when Gohan fights Cell, kicks him around, but refuses to kill
him. This allows Cell to recover and get way stronger than before, making it
very difficult to Gohan to kill him, even with help of other warriors, Vegeta
and even dead Goku. In retrospect, Gohan could have single-handedly kill Cell,
but he didn't do so at the beginning of their fight.

Not by coincidence, this "ability" make every fight involving Saiyan longer
and with plot-twists.

Source: [Zenkai - Dragon Ball Wiki](http://dragonball.wikia.com/wiki/Zenkai)


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Saiyans become more powerful from battle, especially if they're injured. They
also become more powerful every time they are presented with a challenge that
is above them. So when Goku was killed by Picollo (when fighting Raditz) he
became more powerful, even though he had died. Saiyans also become more
powerful through anger and the training from King Kai also helped. As for the
rest of the Z fighters, they always became more powerful from some sort of
training (Kame's lookout, King Kai) or power given to them by a character that
has the ability to unlock their potential (like the elder guru did for Gohan
and Krillin on Namek).


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Aside of Zenkai, which is one of the reasons why Goku increased his power very
fast, another reason is they started to use training under heavy gravity.

Before the battle with Goku, Goku trained with King Kai in a planet with a
gravity 10 times stronger than Earth's. That made him able to increase his
power very fast. Also after that, Goku made Bulma's father to built a device
which created an artificial gravity field of 100 times stronger than the one
of the Earth. With that device and the Zenkai from the battle with Vegeta,
Goku was able to raise his base power level from 9,000 to 90,000. Vegeta also
demanded Bulma's father to create a device with at least created a gravity
field of 300 times stronger of the one on Earth.

Moreover, Goku in particular learnt from King Kai a technique called Kaioken.
With Kaioken he was able to multiply his power level. When he applied kaioken
times 2, he was able to raise his power level from 90,000 to 180,000, in the
battle with Ginyu. But he was able to raise kaioken even up to times 20.

In his battle with Freezer, he was already 3,000,000 in base form due to a
zenkai he got after being beated almost to death and having to recover in the
medical machine. So applying a kaioken times 20 over that, it made him to have
a power level of 60,000,000 during a short period of time.

And aside of that, saiyans have transformations which apply to them
multipliers. The super saiyan transformation has a multiplier of times 50. So
when Goku transformed, a times 50 multiplier was applied to his base form
power of 3,000,000 during that time . Meaning he got a power level of
150,000,000 when fighting with Freezer in super saiyan form.

The power levels of Goku I mention, you can see them stated in this list.

[List of power
levels](https://dragonball.fandom.com/wiki/List_of_Power_Levels)


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