Question

Write in the form of a power with base 6 the following expression

Answer 1

Given:

`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=2^(2n-1)\cdot3^(2n-2)+2^(2n)\cdot3^(2n-2)`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=2^(2n)\cdot3^(2n)\lbrack2^(-1).3^(-2)+3^(-2)\rbrack`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=6^(2n)\lbrack(1)/(2*9)^{}^{}+(1)/(9)\rbrack`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=6^(2n)\lbrack(1+2)/(2*9)^{}\rbrack`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=6^(2n)\lbrack(3)/(18)^{}\rbrack`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=6^(2n)\lbrack(1)/(6)^{}\rbrack`
`2^(2n-1)\cdot9^(n-1)+4^n\cdot3^(2n-2)=6^(2n-1)`