There has to be a rule to adding in base multiplication of bases other than 10

Example

5x2 is 12 in base 8, what appears to be adding 2 . Is this the case for other bases as well always by adding 2?

6 base = 2base6x 3base6 = 8base 6? again as adding.

5 in base 8 is 5 in base 10

2 in base 8 is 2 in base 10

5*2 = 10 in base 10 = 1*10^1+0*10^0

10 = 8+2= 1*8^1+2*8^0 = 12 in base 8

2 base 6 * 3 base 6 = 2 base 10 * 3 base 10 = 6 base 10 = 6 = 1*6^1+0*6^0 = 10 in base 6

suppose you have xyz in base 6 , it means x* 6^2+y*6^1+z*6^0 .( Clearly all x, y,z will be less than 6)

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