Determine the greatest 3-digit number in each base and it desimal (base ten) equivalent? for the following?

Question

base six

base three

bas eleven

Answer 1

1)555   its eq= 5*36+5*6+5=180+30+5=215

2)222    =2*9+2*3+2=18+6+2=26

3)AAA  = A*121+A*11+A=133A=1310  [a=10 but i'm not sure on this one]

Answer 2

First look at base 10. The greatest three-digit number in base 10 is 999₁₀. Following the same pattern, the largest three-digit numbers in  bases 6, 3, and 11 are

555₆

222₃

AAA₁₁, where A=10

Their decimal equivalents:

555₆ = 5×6² + 5×6¹ + 5×6⁰

= 180₁₀ + 30₁₀ + 5₁₀

= 215₁₀

222₃ =  2×3² + 2×3¹ + 2×3⁰

= 18₁₀ + 6₁₀ + 2₁₀

= 26₁₀

AAA₁₁ = =  A×11² + A×11¹ + A×11⁰

= 1210₁₀ + 110₁₀ +10₁₀

= 1330₁₀