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a: Ta có: \(\left(8\cdot5^7+5^6-5^5\right):5^5\)
\(=8\cdot5^2+5-1\)
\(=200+4=204\)
b: Ta có: \(\left(9^{30}-27^{19}\right):3^{57}+\left(125^9-25^{12}\right):5^{24}\)
\(=3^{60}:3^{57}-3^{57}:3^{57}+5^{27}:5^{24}-5^{24}:5^{24}\)
\(=27-1+125-1\)
=150
a. (8,57 - 55 + 56) : 55
= (8,57 : 55) - (55 : 55) + (56 : 55)
= 1,72 - 1 + 5
= 2,89 - 1 + 5
= 6,89
b. (930 - 2719) : 357 + (1259 - 2512) : 524
= (930 : 357) - (2719 : 357) + (1259 : 524) - (2512 : 524)
= 33 - 1 + 125 - 1
= 27 - 1 + 125 - 1
= 150
c. (1012 + 511 . 29 - 513 - 28) : 4 . 55 . 106
= (1012 + 2,5 , 1010 - 513 - 28) : 1,25 . 1010
= (1012 : 1,25 . 1010) + (2,5 . 1010 : 1,25 . 1010) - (513 : 1,25 . 1010) - (28 : 1,25 . 1010)
= 80 + 2 - \(\dfrac{25}{256}\) - \(\dfrac{1}{48828125}\)
= 81,90234373 \(\approx\) 82
ta đặc : \(5^6+5^5+5^4+5^3+5^2+5+1=A\)
vậy ta có : \(A=5^6+5^5+5^4+5^3+5^2+5+1\)
\(\Rightarrow5A=5\left(5^6+5^5+5^4+5^3+5^2+5+1\right)\)
\(5A=5^7+5^6+5^5+5^4+5^3+5^2+5\)
\(\Rightarrow5A-A=4A=\left(5^7+5^6+5^5+5^4+5^3+5^2+5\right)-\left(5^6+5^5+5^4+5^3+5^2+5+1\right)\)
\(4A=5^7-1\Rightarrow A=\dfrac{5^7-1}{4}=19531⋮̸126\)
\(\Rightarrow\) đề sai
\(5^6+5^5+5^4+5^3+5^2+5+1\)
\(=19531\)\(⋮̸\) \(126\)
Vậy \(5^6+5^5+5^4+5^3+5^2+5+1\) không chia hết cho \(126\)
a/A= \(5^6-10^4=5^4.\left(5^2-2^4\right)=5^4.\left(25-16\right)=5^4.9\)chia hết cho 9
b/\(F=5+5^2+5^3+5^4+5^5+5^6=\left(5+5^2+5^3\right).\left(5^4+5^5+5^6\right)=\left(5+25+125\right)\left(5^4+5^5+5^6\right)=155.\left(5^4+5^5+5^6\right)\)
vì 155 chia hết cho 31 đa thức F chia hết cho 31
\(A=\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(4A=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
...
\(4A=5^{64}-1\)
\(\Rightarrow A=\frac{5^{64}-1}{4}>B=\frac{5^{64}-1}{5}\)
1911990403864 nha
chúc bn học tốt
=98,120,100,082.4