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a) 2.84 = 2.(23)4 = 2.212 = 213
b) 256 . 1253 = (52)6 . (53)3 = 512.59 = 521
c) 6255 : 257 = (54)5 : (52)7 = 520:514 = 56
d) 123.33 = (12.3)3 = 363
e) 23.84.163 = 23.(23)4.(24)3 = 23.212.212 = 227
f) 643 . 43 : 163 = (43)3 . 43 : (42)3 = 49.43:46 = 412:46 = 46
G) 812 : ( 32 . 27 ) = (34)2 : 32 . 33 = 38 : 32 . 33 = 36.33 = 39
a) 2 . 84=2.(22)4=2.28=21+8=29
b) 256 . 1253=(22)6.(53)3=212.59=212+9=221
c) 6255 : 257=(54)5:(52)7=520:514=520-14=56
d) 123 . 33=(12.3)3=363
e) 23 . 84 . 163=23.(23)4.(24)3=23.212.212=23+12+12=227
f) 643 . 43 : 163=(43)3.43:(42)3=49.43:46=49+3-6=46
g) 812 : ( 32 . 27 )=(34)2:(32.33)=38:32+3=38:35=38-5=33
a) 24 . 23 = 27 = 128
b) 33 . 3 . 32 = 36 = 729
c) 100.104 = 100 . 10000 = 1000000
d)514 : 512 = 52 = 25
e) 718 : 716 = 72 = 49
f) 39 : 35 = 34 = 81
a) \(2^4.2^3=2^7=128\)
b) \(3^3.3.3^2=3^6=729\)
c) \(100.10^4=10^2.10^4=10^6=1000000\)
d) \(5^{14}:5^{12}=5^2=25\)
e) \(7^{18}:7^{16}=7^2=49\)
f) \(3^9:3^5=3^4=81\)
\(2^5.4=2^5.2^2=2^7\);\(5^4.25=5^4.5^2=5^6\); \(16^3.2^3=\left(2^4\right)^3.2^3=2^{12}.2^3=2^{15}\)
\(625^5:25^7=\left(5^4\right)^5:\left(5^2\right)^7=5^{20}:5^{14}=5^6\); \(25^6:125^3=\left(5^2\right)^6:\left(5^3\right)^3=5^{12}:5^9=5^3\)
\(12^4.3^4=\left(2^2.3\right)^4.3^4=2^8.3^4.3^4=2^8.3^8=6^8\); \(9^6:3^2=\left(3^2\right)^6:3^2=3^{12}:3^2=3^{10}\)
\(2^3.2^4.2=2^8\)
25.84=25.(23)4=25.212=217
256.1253=(52)6.(53)3=512.59=517
6255:257=(54)5:(52)7=520:214=56
a)213
b)521
c)56
d)43
e)227
còn lại tự nghĩ,mệt lắm rùi
a) \(4^{10}.2^{30}=\left(2^2\right)^{10}.2^{30}=2^{2.10}.2^{30}=2^{20}.2^{30}=2^{20+30}=2^{50}\)
b) \(9^{25}.27^4.81^3=\left(3^2\right)^{25}.\left(3^3\right)^4.\left(3^4\right)^3=3^{3.25}.3^{3.4}.3^{4.3}=3^{75}.3^{12}.3^{12}=3^{75+12+12}=3^{99}\)
c) \(25^{50}.125^5=\left(5^2\right)^{50}.\left(5^3\right)^5=5^{2.50}.5^{3.5}=5^{100}.5^{15}=5^{100+15}=5^{115}\)
d) \(64^3.4^8.16^4=\left(4^3\right)^3.4^8.\left(4^2\right)^4=4^{3.3}.4^8.4^{2.4}=4^9.4^8.4^8=4^{9+8+8}=4^{25}\)
e) \(3^8:3^6=3^{8-6}=3^2\)
f) \(2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^{3.3}=2^{10}:2^9=2^{10-9}=2\)
g) \(12^7:6^7=\left(12:6\right)^7=2^7\)
h_ \(21^5:81^3\)kết quả là số dư nên không tính ( đề sai )