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(64 + 27 + 28 + 29 ) : 32
=(64 + 224 ) : 32
=( 26 + 224 ) : 25
= 230 : 25 = 225
a) $3^8:3^6=3^{8-6}=3^2$
$19^7:19^3=19^{7-3}=19^4$
$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$
$12^7:6^7=(12:6)^7=2^7$
$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$
b) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
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 )
1)Đưa về lũy thừa cùng cơ số 2
82= \(\left(2^3\right)^2=2^6\) 323= \(\left(2^5\right)^3=2^{15}\) 644= \(\left(2^6\right)^4=2^{24}\) 43= \(\left(2^2\right)^{^3}=2^6\)
2)Đưa về lũy thừa cùng cơ số 3
93= \(\left(3^2\right)^3=3^6\) 274= \(\left(3^3\right)^4=3^{12}\) 95= \(\left(3^2\right)^5=3^{10}\) 816= \(\left(3^4\right)^6=3^{24}\)
3)Đưa về lũy thừa cùng cơ số 2
83:42= \(\left(2^3\right)^3:\left(2^2\right)^2=2^9:2^4=2^5\) 162:32= \(\left(2^4\right)^2:2^5=2^8:2^5=2^3\)
\(64^4:4^3=\left(2^6\right)^4:\left(2^2\right)^3=2^{24}:2^6=2^{18}\) 323:82= \(\left(2^5\right)^3:\left(2^3\right)^2=2^{15}:2^6=2^9\)
a) 2550 : 1255= (52)50 : (53)5= 5100:515= 585
b) 643. 48 :210= (26)3. (22)8 :210= 218.216:210=224
c) 47.164.642= (22)7.(24)4.(26)2= 214.216.212= 242
d) 38 : 93= 38 : (32)3= 38 : 36= 32
e) 210 : 83= 210 : (23)3= 210 : 29= 2
f) 127 : 67= (2.6)7 : 67= 27.67:67= 27
Những câu còn lại làm tương tự nha
Ta có 78+79+710 = 78.(1+7+72) = 78 . 57 chia hết cho 57
Ta có 1010-109-108 = 108.(102-10-1) = 108 . 89 chia hết cho 89
câu cuối cùng không biết làm
78 . 79 . 710
= 78 . (1+7+72)
= 78 . (1+7+49)
= 78 . 57
vì có một thừa số là 57 nên 78 . 57 chia hết cho 57
suy ra 78 . 79 . 710 chia hết cho 57
\(\left(64+2^7+2^8+2^9\right):32\)
\(=\left(2^6+2^7+2^8+2^9\right):2^5\)
\(=2^5\left(2+2^2+2^3+2^4\right):2^5\)
\(=2+2^2+2^3+2^4\)
\(=30\)
(64+27+28+29):32
=(64+128+256+512):32
=960:32
=30