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a; A = 7^2007-5.7^2005+4.7^2004 chia hết cho 13
A = 7^2004.(7^3 - 5.7 + 4)
A = 7^2004.(343 - 35 + 4)
A = 7^2004.(298 + 4)
A = 7^2004.312
A = 7^2004.13.24
Vì 13 chia hết cho 13 nên A chia hết cho 13 đpcm
Câu 2:Tìm số nguyên x,biết:
a/x-3 chia hết cho 3x-2
Giải
(x - 3) ⋮ (3x - 2)
(3x - 9) ⋮ (3x - 2)
(3x - 2 - 7) ⋮ (3x - 2)
7 ⋮ (3x - 2)
(3x - 2) ∈ Ư(7) = {-7; -1; 1; 7}
\(x\in\) {-5/3; 1/3; 1; 3}
Vì \(x\in\) Z nên \(x\) ∈ {1; 3}
Vậy \(x\) ∈ {1; 3}
Bài 1: Tính bằng 2 cách:
a) 2^5 : 2^4
= 2
b) 3^4 : 3^2
= 3
c) 6^3 : 6^2
= 6
d) 8^4 : 8^2
= 8^2
= 64
e) 7^5 : 7^4
= 7
f) 100^3 : 100
= 100^2
= 10000
Bài 2: Tìm số tự nhiên x, biết:
a) 2^x = 16
2^x = 2^4
x = 4
Vậy x = 4
b) 3^x = 243
3^x = 3^5
x = 5
Vậy x = 5
c) 5^x+1 = 125
5^x + 1 = 5^3
x + 1 = 3
x = 3 - 1
x = 2
Vậy x = 2
a) 27^16 : 9^10
Ta có: (3.9)^16 : 9^10
= 3^16.9^16: 9^10
= 3^16. 9^6
= 3^16.(3^2)^6
=3^16.3^12
=3^28
2^x+1 = 64
2^x + 1 = 2^6
x + 1 = 6
x = 6 - 1
x = 5
Vậy x = 5
b) 1024 = 2^9 : 2^4 + 2.x
1024 = 2^5 + 2\(x\)
1024 = 32 + 2\(x\)
2\(x\) = 1024 - 32
2\(x\) = 992
\(x\) = 992 : 2
\(x\) = 496
Vậy \(x\) = 496
\(3^3\cdot5^3-20\cdot\left\{300-\left[546-2^3\cdot\left(7^8-7^6+7^0\right)\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300-\left[546-2^3\cdot5647153\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300-\left[546-45177224\right]\right\}\)
\(=3^3\cdot5^3-20\cdot\left\{300--45176678\right\}\)
\(=3^3\cdot5^3-20\cdot45176978\)
\(=3375-903539560\)
\(=-903536185\)
\(626500:\left\{50^2:\left[178-4\cdot\left(35-21:3\right)\right]\right\}\)
\(=626500:\left\{50^2:\left[178-4\cdot\left(35-7\right)\right]\right\}\)
\(=626500:\left\{50^2:\left[178-4\cdot28\right]\right\}\)
\(=626500:\left\{50^2:\left[178-112\right]\right\}\)
\(=626500:\left\{50^2:66\right\}\)
\(=626500:\frac{1250}{33}\)
\(=\frac{82698}{5}\)
CHUC BAN HOC TOT >.<
a. 84 : 4 + 39 : 37 + 50
= 21 + 32 + 1
= 21 + 9 + 1
= 21 + 10 = 31
b. 2010 - 2000 : [ 486 - 2.(72 - 6) ]
= 2010 - 2000 : [ 486 - 2.(49 - 6) ]
= 2010 - 2000 : ( 486 - 2.43 )
= 2010 - 2000 : ( 486 - 86 )
= 2010 - 2000 : 400
= 2010 - 5
= 2005
c. 62 - 120 + (-5) - |-5|
= 36 - 120 - 5 - 5
= 36 -
a, 32 x 35 + 32 x 65 b, 150 : [ 25 x ( 18- 42)]
= 32 x ( 35 +65) = 150 : [ 25 x ( 18-16)]
= 9 x 100 = 150 : ( 25 x 2)
= 900 = 150 : 50 = 3
c, 57 : 54 - 21 x 22
= 53- 2 x 4
= 125-8
=117
a) 3 ^ 2 x 35 + 3 ^ 2 x 65 = 9 x 35 + 9 x 65 = 9 x ( 65 + 35 ) = 9 x 100 = 900
j: \(\left(5^7+7^5\right)\left(6^8+8^6\right)\left(2^4-4^2\right)\)
\(=\left(5^7+7^5\right)\left(6^8+8^6\right)\left(16-16\right)\)
\(=0\cdot\left(5^7+7^5\right)\left(6^8+8^6\right)\)
=0
k: \(\left(7^{50}+7^{29}\right)\left(5^{14}+5^{26}\right)\left(3^{35}\cdot3-9^{18}\right)\)
\(=\left(7^{50}+7^{29}\right)\cdot\left(5^{14}+5^{26}\right)\left(3^{36}-3^{36}\right)\)
\(=\left(7^{50}+7^{29}\right)\left(5^{14}+5^{26}\right)\cdot0=0\)