Question

Repede va rog!!! Dau coroana!!!​

Answer 1

f) $(2^{n+3}*3n+2^{n} *3^{n+1} +6^{n}):6^{n} =$

(Scoți factorul comun)

$(2^{3}+3+1)*2^{n} *3^{n} :6^{n} =\\(8+3+1)*2^{n} *3x^{n} :6^{n} =\\12*2^{n} *3^{n} :6^{n}=\\12*6^{n} :6^{n} = \frac{12*6^{n} }{6^{n} }$

(Simplifici fracția cu 6n)

$=\frac{12*1}{1} =12$

(12 ∈ N)

g) $(2^{2n+1}*3^{n} +4^{n} *3^{n+2}):12^{n}=$

(Scoți factorul comun)

$(2n^{2n+1}*3^{n}+2^{2n} *3^{n+2}):12^{n}=\\(2+3^{2})*2^{2n} *3^{n}:12^{n}=\\(2+9)*2^{2n} *3^{n}:12^{n}=\\11*2^{2n} *3^{n} :12^{n} =\\\frac{11*2^{2n}*3^{n}}{12^{n}}=\\\frac{11*4^{n}*3^{n}}{6^{n}*2^{n}}=\\\frac{11*2^{2n}*3^{n} }{3^{n} *2^{n} *2^{n} }=$

(Simplifici fracția cu 3n și cu 2n)

$\frac{11*2^{n} }{2^{n}}=$

(Simplifici iar cu 2n)

$=11$

(11 ∈ N)

h)

$(2^{3n+1} *9^{n}+8^{n}*3^{2n+1} +6^{2n} *2^{n+3}):13=\\(2^{3n+1} *3^{2n} +2^{3n} *3^{2n+1} +3^{2n} *2^{2n} *2^{n+3}):13 =$

(Scoți factorul comun)

$(2^{3n} +1*3^{2n} +2^{3n} *2^{2n+1} +3^{2n} *2^{3n+3}):13=\\(2+3+2^{3} )*2^{3n} *3^{2n}:13=\\(2+3+8)*2^{3n} *3^{2n} :13=\\13*2^{3n} *3^{2n} :13=$

(Împarți expresia la ea însăși, 13:13=1)

$1*2^{3n} *3^{2n} =\\8^{n}*9^{n}= (8*9)^{n} =72^{n}$