a) 7^6 + 7^5 - 7^4
= 7^4.(7^2 + 7 - 1)
= 7^4.(49 + 7 - 1)
= 7^4.55
= 7^4.5.11 ⋮11(đpcm)
b) 10^9 + 10^8 + 10^7
= 10^7.(10^2 + 10 + 1)
= 5^7.2^7.(100 + 10 + 1)
= 5^7.2^6.2.111
= 5^7.2^6.222 ⋮222(đpcm)
Chung minh rang
a,76+75-74\(⋮\)11
b,109+108+107\(⋮\)222
1 tính
a. \((\left|-5\right|7^4+3^2.2\dfrac{2}{5}):(7^5.125.7^3.50)\)
b. \((\dfrac{3^2}{9}.\dfrac{3^3}{81})^{12}:(\dfrac{3^6}{81^2})^{10}\)
c. \([(\dfrac{1}{2})^2.(\dfrac{1}{3})^4.\dfrac{2}{7}]:\left(\dfrac{1}{3}\right)^{-2}.\dfrac{-2^2}{7}\)
Cho E=2^15.0,5^5+3.2^10/2^11.2^3-2^15:2^3 Cho F=2.6^7+6^8/2^5.9^4-2.3^7+3^8 Cho G=4^5.9^4-2.6^9/2^10.3^8+6^8.20
a)\(\frac{45^{10}.5^{10}}{75^{10}}\)
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}\)
c)\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
d) \(\frac{14^{16}.21^{32}.45^{48}}{10^{16}.15^{32}.7^{96}}\)
Trong vở bài tập của bạn Dũng có bài làm sau :
a) \(\left(-5\right)^2.\left(-5\right)^3=\left(-5\right)^6\)
b) \(\left(0,75\right)^3:0,75=\left(0,75\right)^2\)
c) \(\left(0,2\right)^{10}:\left(0,2\right)^5=\left(0,2\right)^2\)
d) \(\left[\left(-\dfrac{1}{7}\right)^2\right]^4=\left(-\dfrac{1}{7}\right)^6\)
e) \(\dfrac{50^3}{125}=\dfrac{50^3}{5^3}=\left(\dfrac{50}{5}\right)^3=10^3=1000\)
Hãy kiểm tra lại các đáp số và sửa lại chỗ sai (nếu có)
f) \(\dfrac{8^{10}}{4^8}=\left(\dfrac{8}{4}\right)^{10-8}=2^2\)
C/m rằng : a,( 10^19+10^18+10^17 ) chia hết 555; b, ( 81 ^7 - 27^9 - 9^13) chia hết cho 15; c, ( 4^13 + 32^5 - 8^8 ) chia hết cho 5 giup mk vs nhé
\(\dfrac{8^5.\left(-5\right)^8+\left(-2\right)^5.10^9}{2^{16}.5^7+20^8}\) giúp mình nha cảm ơn mọi người
1) Chứng minh rằng :
a) 817-279+329\(⋮\)33
b) 109+108+107\(⋮\)55
c)\(\dfrac{9^{11}-9^{10}-9^9}{639}\in N\)
d)817-279-913\(⋮\)45
2) Tìm x \(\in\) N*
a)27<3x<3.81
b)415.915<2x.3x<1816.216
c)(2x-1)6=(2x-1)8
Các bạn giúp mình nha 
Tính: \(\dfrac{2^{19}\cdot27^3-15\cdot\left(-4\right)^9\cdot9^4}{6^9\cdot2^{10}+\left(-12\right)^{10}}\)
