\(8^5+16^4=\left(2^3\right)^5+\left(2^4\right)^4=2^{15}+2^{16}=2^{15}.1+2^{15}.2=2^{15}\left(2+1\right)=2^{15}.3\)

Vậy tổng chia hết cho 3

\(2^8+2^9+2^{10}=2^8.1+2^8.2+2^8.2^2=2^8.\left(1+2+4\right)=2^8.7\)

Vậy tổng chia hết cho 7

Ta có:

\(8^5+4^7-16^3=\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\)

\(=2^{15}+2^{14}-2^{12}\)

\(=2^4.\left(2^{11}+2^{10}-2^8\right)=16.\left(2^{11}+2^{10}-2^8\right)\)

Vì 16 chia hết cho 16 nên \(16.\left(2^{11}+2^{10}-2^8\right)\) chia hết cho 16

Do đó \(8^5+4^7-16^3\)chia hết cho 16 (đpcm)

Chúc bạn học tốt!!!

\(8^5+4^7-16^3\\ =\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\\ =2^{15}+2^{14}-2^{12}\\ =2^{12}\cdot\left(2^3+2^2-1\right)\\ =2^{4\cdot3}\cdot\left(8+4-1\right)\\ =\left(2^4\right)^3\cdot11\\ =16^3\cdot11⋮16\)

Vậy \(8^5+4^7-16^3⋮16\)

\(8^5+4^7-16^3\)

\(=\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\)

\(=2^{15}+2^{14}-2^{12}\)

\(=2^{12}.2^3+2^{12}.2^2-2^{12}.1\)

\(=2^{12}\left(2^3+2^2-1\right)\)

\(=2^{12}\left(8+4-1\right)\)

\(=2^{12}.11\)

\(=\left(2^4\right)^3.11\)

\(=16^3.11⋮16\rightarrowđpcm\)

\(=2^{15}+2^{14}-2^{12}=2^4\left(2^{11}+2^{10}-2^8\right).\) chia hết cho 16

ta thấy : 8⁵ ; 4⁷ ; 16³ deu chia hết cho 16

=> 8⁵+4⁷-16³ chia het cho 16  

Ta có:

8⁵=(4.2)⁵=4⁵.2⁵=4²⁺²⁺¹.(2²)^2,5=(4².4².4).4^2,5=(16.16.4).4².4^0.5=[(16².4).16.2]>16³và chia hết cho 16

4⁷=4²⁺⁵=4².4⁵=(16.4⁵) chia hết cho 16

16³chia hết cho 16

Vậy (8⁵+4⁷-16³) chia hết cho 16

ai nhanh mình k

1 /2 -1 /4 + 1 /8-1 /16 + 1 /32-1 /64 < 1 /3

Cách 1:21/64 < 1/3

Cách 2:21/64 < 0.(3)

Đúng

1 /2 + 1 /4 + 1 /8 + 1 /16 + 1 /32 + 1 /64 < 1 /3

Cách 2:63/64 < 0.(3)

Ko đúng

Câu 3 mình ko biết

a)cho \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)là A

ta có:A=\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\)

2A=\(\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\right)2\)

2A=\(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\)

2A+A=\(\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}\right)\)

3A=\(1-\frac{1}{64}\Rightarrow3A=\frac{63}{64}\Rightarrow A=\frac{21}{64}< \frac{1}{3}\)

vậy \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)

b) sai đề (\(\frac{63}{64}< \frac{1}{3}\)hay sao)

c)sai nối (nếu x=y=3 thì 2x+3y=17 chia hết nhưng 9x+5y=42 ko chia hết)

Ta có \(8^5+4^7-16^3\)

\(=\left(2^3\right)^5+\left(2^2\right)^7-\left(2^4\right)^3\)

\(=2^{15}+2^{14}-2^{12}\)

\(=2^8\left(2^7+2^6-2^4\right)\)

\(=256\left(2^7+2^6-2^4\right)⋮256\)

Vậy \(8^5+4^7-16^3⋮256\left(đpcm\right)\)

Chúc bn học tốt

cho mik hỏi câu này nữa   a= 2+2 mũ 3 + 2 mũ 5 +.....+2 mũ 51