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a) 25 : 23
C1: 25 : 23
= 32 : 8
= 4
C2: 25 : 23
= 25 - 3
= 22 = 4
b) 35 : 32
C1: 35 : 32
= 243 : 9
= 27
C2: 35 : 32
= 35 - 2
= 33 = 27
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a) \(\left(3^5\times3^7\right):3^{10}+5\times2^4-7^3:7=3^{12}:3^{10}+5\times2^4-7^2\)
\(=3^2-5\times16-7^2=9-80-49=-120\)
b) \(15:\left(3^5:3^4\right)-2^9:2^7=15:3-2^2=5-4=1\)
c)\(5\times3^5:\left(3^8:3^5\right)-2^3\times5=5\times3^5:3^3-2^3\times5\)
\(=5\times3^2-2^3\times5=5\times9-8\times5=45-40=5\)
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A . 33 : 3 + 52 : 5 - 079 + 25 0 + 1n
B. 72 : 7 + 33 : 32 + 19898 + 1
C. 105 : 102 + 105 : 105
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a) 2 . [ ( 95 + 52 : 5 ) : 22 + 180 ] - 22 . 102
= 2 . [ ( 95 + 5 ) : 4 + 180 ] - 202
= 2 . ( 100 : 4 + 180 ) - 400
= 2 . ( 25 + 180 ) - 400
= 2 . 205 - 400
= 410 - 400
= 10
b) 34 . 2 + 23 . 5 - 7 ( 57 : 55 )
= 81 . 2 + 8 . 5 - 7 . 25
= 162 + 40 + 175
= 377
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\(\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\frac{2^{11}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^2}{3}=\frac{4}{3}\)
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a)3 . 103 + 2 . 102 + 5 . 10
= 3 . 102 . 10 + 2 . 10 . 10 + 5 . 10
= 10 . ( 3 . 102 + 2 . 10 + 5 )
= 10 . ( 3 . 100 + 20 + 5 )
= 10 . ( 300 + 20 + 5 )
= 10 . 325
= 3250
a) 3 . 103 + 2 . 102 + 5 . 10
= 3 . 1000 + 2 . 100 + 5 . 10
= 3000 + 200 + 50
= 3250
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b) 3^2 . [(5^2 - 3 ) : 11 ] - 2^4 + 2.10^3
= 9 . [(25 - 3 ) : 11 ] - 16 + 2.1000
= 9 . [22 : 11 ] - 16 + 2000
= 9 . 2 - 16 + 2000
= 18 - 16 + 2000
= 2 + 2000
= 2002
(72005 + 72004) : 72004
= 72005 : 72004 + 72004 : 72004
= 72005 - 2004 + 1
= 71 + 1
= 7 + 1
= 8
a) ( 3^5 . 3^7 ) : 3^10 + 5.2^4 - 7^3 : 7
= 3^10 : 3^10 + 80 - 7^2
= 1 + 80 - 49
= 32
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