Răspuns:
Explicație pas cu pas:
a)
[tex]2^3 \cdot4^3 = 2^3\cdot(2^2)^3 = 2^3\cdot2^{2\cdot3} = 2^3\cdot2^{6} =2^{3+6} = 2^9[/tex]
b)
[tex]2^7 \cdot16 = 2^7\cdot2^4 =2^{7+4} = 2^{11}[/tex]
c)
[tex]2^{25}\cdot4^{11} \cdot8^7 =2^{25}\cdot(2^2)^{11} \cdot(2^3)^7 =2^{25}\cdot2^{2\cdot11} \cdot2^{3\cdot7} =\\\\=2^{25}\cdot2^{22} \cdot2^{21} =2^{25 + 22 + 21} =2^{68}[/tex]
d)
[tex]9^{2}\cdot27^{3} \cdot3^7 =(3^2)^2\cdot(3^3)^{3} \cdot3^7 =3^{2\cdot2}\cdot3^{3\cdot3} \cdot3^{7} =\\\\=3^{4}\cdot3^{9} \cdot3^{7} = 3^{4+9+7} = 3^{20}[/tex]
e)
[tex]4^{22} \cdot2^{40} = (2^{2})^{22}\cdot2^{40}= 2^{22\cdot2}\cdot2^{40} = 2^{44}\cdot2^{40} =2^{44+40} = 2^{84}[/tex]
f)
[tex]3^{6}\cdot4^{6} :12^4 =3^6\cdot4^{6} :(4\cdot3)^4 =3^{6}\cdot4^{6} :(4^4\cdot3^{4})=\\\\=3^{6}\cdot4^{6} :4^4:3^{4}=3^{6-4}\cdot4^{6-4} = 3^{2}\cdot4^{2}=(3\cdot4)^2 = 12^2[/tex]
g)
[tex](5^{10}\cdot25^{2})^3:5^{40} = [5^{10}\cdot(5^2)^{2}]^3:5^{40} = (5^{10}\cdot5^{2\cdot2})^3:5^{40} = (5^{10}\cdot5^{4})^3:5^{40} =\\\\ =(5^{10+4})^3:5^{40}= (5^{14})^3:5^{40}= 5^{14\cdot3}:5^{40} = 5^{42}:5^{40} = 5^{42-40} = 5^2[/tex]
h)
[tex]125^6 : 25^4 \cdot (5^3)^{11} = (5^3)^6 : (5^2)^4 \cdot (5^3)^{11} = 5^{3 \cdot 6} : 5^{2 \cdot 4} \cdot 5^{3 \cdot 11} = 5^{18} : 5^{8} \cdot 5^{33} =\\\\= 5^{18-8+33} = 5^{43}[/tex]
