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$$2^{2n-1}\cdot9^{n-1}+4^n\cdot3^{2n-2}=6^{2n}\lbrack\frac{1}{2\times9}^{}^{}+\frac{1}{9}\rbrack$$2^{2n-1}\cdot9^{n-1}+4^n\cdot3^{2n-2}=6^{2n}\lbrack\frac{1+2}{2\times9}^{}\rbrack$$2^{2n-1}\cdot9^{n-1}+4^n\cdot3^{2n-2}=6^{2n}\lbrack\frac{3}{18}^{}\rbrack$$2^{2n-1}\cdot9^{n-1}+4^n\cdot3^{2n-2}=6^{2n}\lbrack\frac{1}{6}^{}\rbrack$$2^{2n-1}\cdot9^{n-1}+4^n\cdot3^{2n-2}=6^{2n-1}$