\(\left[3^{22}\cdot\left(3^8:3^3\right)+2\cdot3^{27}\right]:3^{26}\\ =\left(3^{22}\cdot3^5+2\cdot3^{27}\right):3^{26}\\ =3^{27}\left(1+2\right):3^{26}\\ =3^{27}\cdot3:3^{26}\\ =3^2=9\)

\(\left[3^{22}.\left(3^8:3^3\right)+2.3^{27}\right]\):\(3^{26}\)

=\(\left(3^{22}.3^5+2.3^{27}\right):3^{26}\)

=(\(3^{27}\)+2.\(3^{27}\)):\(3^{26}\)

=\(3^{27}\).(1+2):\(3^{26}\)

=\(3^{28}:3^{26}=3^2\)=9

 3²¹ + 3²² + 3²³ + 3²⁴ + 3²⁵ +3²⁶ + 3²⁷ +  3²⁸ + 3²⁹  

^{= \(3^{21}.\left(1+3+3^2\right)+3^{24}.\left(1+3+3^2\right)+3^{27}.\left(1+3+3^2\right)\)}

^{= \(3^{21}.13+3^{24}.13+3^{27}.13\)}

^{= \(13.\left(3^{21}+3^{24}+3^{27}\right)\)}

^{vì   \(13⋮13\)} nên \(13.\left(3^{21}+3^{24}+3^{27}\right)⋮13\)

vậy 3²¹ + 3²² + 3²³ + 3²⁴ + 3²⁵ +3²⁶ + 3²⁷ +  3²⁸ + 3²⁹  chia hết cho 13

Sửa đề: \(\frac{2\cdot4^{14}\cdot9^8-3^{17}\cdot8^9}{19\cdot2^{26}\cdot3^{13}-27^5}\)

Ta có: \(\frac{2\cdot4^{14}\cdot9^8-3^{17}\cdot8^9}{19\cdot2^{26}\cdot3^{13}-27^5\cdot2^{24}}\)

\(=\frac{2\cdot\left(2^2\right)^{14}\cdot\left(3^2\right)^8-3^{17}\cdot\left(2^3\right)^9}{19^{}\cdot2^{26}\cdot3^{13}-\left(3^3\right)^5\cdot2^{24}}\) \(=\frac{2^{29}\cdot3^{16}-3^{17}\cdot2^{27}}{19\cdot2^{26}\cdot3^{13}-3^{15}\cdot2^{24}}=\frac{2^{27}\cdot3^{16}\left(2^2-3\right)}{2^{24}\cdot3^{13}\left(19\cdot2^2-3^2\right)}\)

\(=\frac{2^3\cdot3^3}{19\cdot4-9}=\frac{8\cdot9}{76-9}=\frac{72}{67}\)

Sửa đề: \(\frac{2\cdot4^{14}\cdot9^8-3^{17}\cdot8^9}{19\cdot2^{26}\cdot3^{13}-27^5}\)

Ta có: \(\frac{2\cdot4^{14}\cdot9^8-3^{17}\cdot8^9}{19\cdot2^{26}\cdot3^{13}-27^5\cdot2^{24}}\)

\(=\frac{2\cdot2^{28}\cdot3^{16}-3^{17}\cdot2^{27}}{19\cdot2^{26}\cdot3^{13}-3^{15}\cdot2^{24}}\)

\(=\frac{2^{27}\cdot3^{16}\left(2^2-3\right)}{3^{13}\cdot2^{24}\cdot\left(19\cdot2^2-3^2\right)}=\frac{2^3\cdot3\cdot1}{76-9}=\frac{24\cdot3}{67}=\frac{72}{67}\)

tu lam di

\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{22.3^{28}-3^{28}.2}{2^3.3^{28}}=\frac{3^{28}.20}{3^{28}.4}=\frac{20}{4}=5\)

cách hả?

bấm máy cx thừa sức

mik cũng đg cần câu naỳ

I cũng vậy

sao bài 3 phần a hình như sai đề bài rồi đó

1,2 dễ ko làm

3,

S = 1 + 2 + 2² + 2³ + ... + 2⁹

2S = 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰

2S - S = ( 2 + 2² + 2³ + 2⁴ + ... + 2¹⁰ ) - ( 1 + 2 + 2² + 2³ + ... + 2⁹ )

S = 2¹⁰ - 1

Mà 5 . 2⁸ = ( 1 + 2² ) . 2⁸ = 2⁸ + 2¹⁰ > 2¹⁰ > 2¹⁰ - 1

Vậy S < 5 . 2⁸

P = 1 + 3 + 3² + 3³ + ... + 3²⁰

3P = 3 + 3² + 3³ + 3⁴ +  ... + 3²¹

3P - P = ( 3 + 3² + 3³ + 3⁴ +  ... + 3²¹ ) - ( 1 + 3 + 3² + 3³ + ... + 3²⁰ )

2P = 3²¹ - 1

P = ( 3²¹ - 1 ) : 2 < 3²¹

Vậy P < 3²¹