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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) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
101 - {36 + [7 . 32 - 24 : 3 + ( 9 - 7)3 ]} : 32
= 101 - [36 + (7 . 9 - 24 : 3 + 23)] : 9
= 101 - [36 + (63 - 8 + 8)] : 9
= 101 - (36 + 63) : 9
= 101 - 99 : 9
= 101 - 11 = 90
trả lời :
101 - {36 + [7 . 32 - 24 : 3 + ( 9 - 7)3 ]} : 32
= 101 - [36 + (7 . 9 - 24 : 3 + 23)] : 9
= 101 - [36 + (63 - 8 + 8)] : 9
= 101 - (36 + 63) : 9
= 101 - 99 : 9
= 101 - 11 = 90
a) 205 – [1200 – (42 – 2.3)3] : 40
= 205 – [1200 – ( 16 - 6 )3 ] : 40
= 205 – [1200 – ( 10 )3 ] : 40
= 205 – [1200 – 1000 ] : 40
= 205 – 200 : 40
= 205 – 50
= 155
b) 177 :[2.(42 – 9) + 32(15 – 10)]
= 177 :[2.(16 – 9) + 9. 5]
= 177 :[2.7 + 9. 5]
= 177 :[ 14 + 45 ]
= 177 : 59
= 3
J.
=2345-1000:[19-2*(3^2)]
=2345-1000:[19-18]
=2345-1000:1
=2345-1000
=1345
F.
=(11^2)-(3^2)*-3+50
=[(11-3)^2]*-3+50
=(8^2)*-3+50
=64-3+50
=61+50
=111
E.
=295+(31-4*5)
=295+(31-20)
=295+11
=306
mik het bit làm r
J. 2345-1000 : [ 19 - 2 ( 21 - 18 )2 ]
= 2345 - 1000 : [ 19 - 2.32 ]
= 2345 - 1000 : (19 - 18)
= 2345 - 1000
= 1345.
F. 1125 : 1123 - 33 + 50
= 112 - 27 + 50
= 121 - 27 + 50
= 144
E. 295 + ( 31 - 22 . 5 )2
= 295 + (31 - 4.5)2
= 295 + 112
= 295 + 121
= 416
H. 47 + ( 45 . 24 - 52 . 12) : 14
= 47 + (45 . 16 - 25.12) : 14
= 47 + 420 : 14
= 47 + 30
= 77
I. 102 - 60 : ( 56 : 54 - 3 . 5 )
= 100 - 60 : (25 - 15)
= 100 - 60 : 10
= 100 - 6
= 94.
K. 205 + [ 1200 - ( 42 - 2 . 3 ) 3 ] : 40
= 205 + [1200 - (16 - 6)3 ] : 40
= 205 + [1200 - 1000] : 40
= 205 + 200 : 40
= 205 + 5
= 210
L. 500 - { 5 . [ 409 - ( 23 . 3 - 21 ) 2 ] + 103 } : 15
= 500 - {5 . [409 - (24 - 21)2 ] + 1000} : 15
= 500 - {5 . [409 - 9] + 1000}: 15
= 500 - {5.400+1000}:15
= 500 -3000:15
= 500 - 200
= 300.
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 )
\(500-\left\{5\left[409-\left(2^3^{ }.3-21\right)^2\right]+10^3\right\}:15\)\(5\)
\(=500-\left\{5\left[409-\left(8.3-21\right)^2\right]+1000\right\}:15\)
\(=500-\left\{5\left[409-\left(24-21\right)^2\right]+1000\right\}:15\)
a) \(500-\left\{5.\left[409-\left(2^3.3-21\right)^2+10^3\right]\right\}:25\)
\(=500-\left\{5.\left[409-9+1000\right]\right\}:25\)
\(=500-\left\{5.1400\right\}:25\)
\(=500-280=220\)
b) \(\left(9^3.2^{10}.27^5\right):\left(4^5.81^6\right)\)
\(=\left(3^{21}.2^{10}\right):\left(2^{10}.3^{24}\right)=3^{-3}=\frac{1}{27}\)