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52 . 57 = 52 + 7 = 59
75 . 7 = 7 . 7 . 7 . 7 . 7 . 7 = 76
5^6+5^7+5^8
=5^6.(1+5+5^2)
=5^6.31 chia hết cho 31
7^6+7^5-7^4
=7^4.(7^2+7-1)
=7^4.55 chia hết cho 11
BÀI 2:
a) \(5^6+5^7+5^8=5^6\left(1+5+5^2\right)=5^6.31\) \(⋮\)\(31\)
b) \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.55\)\(⋮\)\(11\)
c) \(2^3+2^4+2^5=2^3.\left(1+2+2^2\right)=2^3.7\)\(⋮\)\(7\)
d) mk chỉnh đề
\(1+2+2^2+2^3+...+2^{59}\)
\(=\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{58}+2^{59}\right)\)
\(=\left(1+2\right)+2^2\left(1+2\right)+...+2^{58}\left(1+2\right)\)
\(=\left(1+2\right)\left(1+2^2+...+2^{58}\right)\)
\(=3\left(1+2^2+...+2^{58}\right)\)\(⋮\)\(3\)
\(a)3^9:3^6=3^3\)
\(b)16^{2000}:8^{90}\)
\(=16^{2000}:16^{45}\)
\(=16^{1955}\)
\(a,3^9:3^6=3^3\)
\(b,16^{2000}:8^{90}=\left(16^3\right)^{\frac{200}{3}}:\left(8^4\right)^{\frac{45}{2}}4096^{\frac{200}{3}}:4096^{\frac{45}{2}}=4096^{\frac{265}{6}}\)
1
a.a.a.b.b=\(a^3.b^2\) ,m.m.m.m+p.p=\(m^4+p^2\)
\(a^3.a^5=a^8\) ,\(x^7.x.x^4=x^{12}\),\(m4^6:4^6=m\)
2
\(2^{3^2}=64\)
3
3x=\(3^3.3^5\)(=)3x=\(3^8\)(=)x=\(3^7\)
\(2^x=2^2.2^7\)(=)\(2^x=2^9\)=>x=9
2x.3x=1(=)6 \(x^2\)=1(=)\(x^2\)=\(\frac{1}{6}\)(=)x ko tồn tại
a/ 440 + 2 [ 125 - x ] = 546
==> 2 [ 125 - x ] = 546 - 440
==> 2 [ 125 - x ] 106
==> 125 - x = 106 : 2
==> 125 - x = 53 ==> x = 125 - 53 =72
b/ 7x - 33 = 27 : 24
==> 7x - 27 = 27-4 = 23 = 8
==> 7x = 8+ 27
==> 7x = 35 ==> x = 35 : 7 = 5
c/ [ 12x - 43 ] . 83 = 4 . 84
==> [ 12x - 26 ] . 29 = 22 . 212
==> [ 12x - 26 ] . 29 = 214
==> [ 12x - 26 ] = 214 : 29 = 25
==>. 12x = 25 + 26 = 96
==> x = 96 : 12 = 8
d/ 123 - 5. [ x + 4 ] = 38
==> 5. [ x + 4 ] = 123 - 38
==> 5. [ x + 4 ] = 85
==> x + 4 = 85 : 5
==> x + 4 = 17
==> x = 17 - 4 = 13
e/ [ 2600 + 6400 ] - 3.x = 1200
==> 9000 - 3x = 1200
==> 3x = 9000 -1200 = 7800
==> x = 7800 : 3 = 2600
f/ x2 - 72 : 36 = 23
==> x2 - 2 = 23
==> x2 = 23 + 2
==>x2 = 25
==> x2 = 52
==> x = 5
ko bt