f) [tex](2^{n+3}*3n+2^{n} *3^{n+1} +6^{n}):6^{n} =\\[/tex]
(Scoți factorul comun)
[tex](2^{3}+3+1)*2^{n} *3^{n} :6^{n} =\\(8+3+1)*2^{n} *3x^{n} :6^{n} =\\12*2^{n} *3^{n} :6^{n}=\\12*6^{n} :6^{n} = \frac{12*6^{n} }{6^{n} }[/tex]
(Simplifici fracția cu 6n)
[tex]=\frac{12*1}{1} =12[/tex]
(12 ∈ N)
g) [tex](2^{2n+1}*3^{n} +4^{n} *3^{n+2}):12^{n}=\\[/tex]
(Scoți factorul comun)
[tex](2n^{2n+1}*3^{n}+2^{2n} *3^{n+2}):12^{n}=\\(2+3^{2})*2^{2n} *3^{n}:12^{n}=\\(2+9)*2^{2n} *3^{n}:12^{n}=\\11*2^{2n} *3^{n} :12^{n} =\\\frac{11*2^{2n}*3^{n}}{12^{n}}=\\\frac{11*4^{n}*3^{n}}{6^{n}*2^{n}}=\\\frac{11*2^{2n}*3^{n} }{3^{n} *2^{n} *2^{n} }=[/tex]
(Simplifici fracția cu 3n și cu 2n)
[tex]\frac{11*2^{n} }{2^{n}}=[/tex]
(Simplifici iar cu 2n)
[tex]=11[/tex]
(11 ∈ N)
h)
[tex](2^{3n+1} *9^{n}+8^{n}*3^{2n+1} +6^{2n} *2^{n+3}):13=\\(2^{3n+1} *3^{2n} +2^{3n} *3^{2n+1} +3^{2n} *2^{2n} *2^{n+3}):13 =\\[/tex]
(Scoți factorul comun)
[tex](2^{3n} +1*3^{2n} +2^{3n} *2^{2n+1} +3^{2n} *2^{3n+3}):13=\\(2+3+2^{3} )*2^{3n} *3^{2n}:13=\\(2+3+8)*2^{3n} *3^{2n} :13=\\13*2^{3n} *3^{2n} :13=\\[/tex]
(Împarți expresia la ea însăși, 13:13=1)
[tex]1*2^{3n} *3^{2n} =\\8^{n}*9^{n}= (8*9)^{n} =72^{n}[/tex]
