From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Dragon Ball GT
10x Kamehameha was first developed by Goku while battling a Baby-possessed Vegeta. Despite being at Super Saiyan 4, Goku began to struggle after Super Baby Vegeta transformed into a Great Ape. Midway into their fight, Goku rose into the air, united two energy spheres in his hands and unleashed the 10x Kamehameha for the first time. Despite its massive power, the attack inflicted little damage to Baby. Shortly thereafter, the delayed effect of the technique kicked in and the Tsufruian parasite was paralyzed temporarily, sending him plummeting to the ground (this side-effect is completely absent from video game incarnations of the technique, which fundamentally make the 10x Kamehameha no different from a normal energy wave). Later during the fight, Great Ape Baby launched a Revenge Death Ball Final at Goku, who retaliated by absorbing its massive power and returning it in the form of a powerful 10x Kamehameha, severely damaging Baby. Goku later used the 10x Kamehameha to blast Baby's spaceship hurdling into the Sun during his attempt to escape, killing the Tsufruian parasite.
Super 17 Saga
The 10x Kamehameha was next used by Goku against Super 17, who responded by merely absorbing the energy. In the Shadow Dragon Saga, Goku used the 10x Kamehameha against the evil Shadow Dragons while searching for the Dragon Balls with his granddaughter Pan. Later during his battle with Syn Shenron, Goku, again in his Super Saiyan 4 transformation, launched a 10x Kamehameha head-on, which evidently had no effect on the Shadow Dragon. In the ensuing battle with Omega Shenron, Goku retaliated with a combination of the 10x Kamehameha and Dragon Fist techniques, which the Shadow Dragon survived by regenerating.
The 10x Kamehameha debuted in Dragon Ball Z: Budokai 3 when using Super Saiyan 4 Goku and is a replacement for the normal Kamehameha. It is a tad slower in preparation, but is ridiculously powerful and is enough to take out a entire health bar (1000 points) or more if done correctly. It changes automatically if you become a Super Saiyan 4 as Goku.
It later appeared in Dragon Ball Heroes.
- A common misconception is that the Japanese name for the attack is "Jūbei Kamehameha". The Kanji for "times" (倍), as in "10 times", is actually pronounced "bai". The confusion arises due to Goku's way of speaking. Due to his unique dialect and accent (his idiolect) in Japanese, it is heard as "bei". Goku's way of speaking is to show he is uneducated, or "hick-ish". In Goku's idiolect, vowels are switched constantly. This is seen when Goku says "ora" instead of "ore" or "omei/omee" instead of "omae". Likewise, "Jūbai" becomes "Jūbei" when spoken by Goku.
- Throughout the Dragon Ball series, it has been canonically stated that a Saiyan's battle power is multiplied times ten when transformed into a Great Ape. Since the Super Saiyan 4 state is by technicality a condensed version of the Golden Great Ape form, it is possible that this fact is what gave birth to the 10x Kamehameha.
- The 10x Kamehameha and Crimson Galick Gun (in which the latter is used by Vegeta in his Super Saiyan 3 form in Dragon Ball: Raging Blast) both share similarities. They are both reddish-orange in color, a more powerful version of a character's signature technique (Kamehameha for Goku and Galick Gun for Vegeta), and are created upon the creator achieving a new form of Super Saiyan (Super Saiyan 4 for Goku and Super Saiyan 3 for Vegeta).
- In its first use during the Baby Saga, the 10x Kamehameha is whitish-blue in appearance, much like the standard one. In later uses, it emits a crimson aura instead.
- The first time Super Saiyan 4 Goku attempts the 10x Kamehameha, he needs to charge two energy spheres and merge them together. Later on in the series, he charges the 10x Kamehameha like a Super Kamehameha.