B=1+3+3²+...+3¹⁰

3B=3(1+3+3²+...+3¹⁰)

3B=3+3²+3³+...+3¹¹

3B-B=(3+3²+3³+...+3¹¹)-(1+3+3²+...+3¹⁰)

2B=3¹¹-1

B=\(\frac{3^{11}-1}{2}\)

B=88573

Bài làm:

a) \(a=2+2^3+2^5+...+2^{99}+2^{101}\)

\(\Rightarrow4a=2^3+2^5+2^7+...+2^{101}+2^{103}\)

\(\Rightarrow4a-a=\left(2^3+2^5+2^7+...+2^{103}\right)-\left(2+2^3+2^5+...+2^{101}\right)\)

\(\Leftrightarrow3a=2^{103}-2\)

\(\Rightarrow a=\frac{2^{103}-2}{3}\)

Vậy \(a=\frac{2^{103}-2}{3}\)

b) \(b=1-5^3+5^6-5^9+...+5^{96}-5^{99}\)

\(\Rightarrow125b=5^3-5^6+5^9-5^{12}+...+5^{99}-5^{102}\)

\(\Rightarrow125b+b=\left(5^3-5^6+5^9-5^{12}+...+5^{99}-5^{102}\right)+\left(1-5^3+5^6-5^9+...+5^{96}-5^{99}\right)\)

\(\Leftrightarrow126b=1-5^{102}\)

\(\Rightarrow b=\frac{1-5^{102}}{126}\)

Vậy \(b=\frac{1-5^{102}}{126}\)

Học tốt!!!!

\(A=4+4^2+...+4^{99}\)

\(\Rightarrow4A=4^2+3^3+...+4^{99}+4^{100}\)

\(\Rightarrow4A-A=4^{100}-4\)

\(\Rightarrow3A=4^{100}-4\Rightarrow A=\frac{4^{100}-4}{3}\)

\(B=5+5^2+...+5^{10}\)

\(5B=5^2+5^3+...+5^{10}+5^{11}\)

\(5B-B=4B=5^{11}-5\Rightarrow B=\frac{5^{11}-5}{4}\)

C đang 6 mũ sao tự nhiên nhảy đâu ra 9 mũ?

Nếu nó là 6 mũ thì làm tương tự như 2 câu trên

Ai đó help me mai lộp rồi

a,3¹² và 5⁸

Ta có:3¹²=(3³)⁴=27⁴

5⁸=(5²)⁴=25⁴

Vì 27⁴>25⁴ nên 3¹²>5⁸

b,(0,6)⁹ và (0,9)⁶

Ta có:(0,9)⁶>(0,6)⁶ mà (0,6)⁶>(0,6)⁹

\(\Rightarrow\)(0,6)⁹<(0,9)⁶

c,5²⁰⁰⁰ và 10¹⁰⁰⁰

Ta có:5²⁰⁰⁰=(5²)¹⁰⁰⁰=25¹⁰⁰⁰>10¹⁰⁰⁰

\(\Rightarrow\)5²⁰⁰⁰>10¹⁰⁰⁰

d,?????

a: =5-78*32

=5-2496

=-2491

b: \(=6\left(9-6\right)=6\cdot3=18\)

c: \(=46\cdot\dfrac{\left(123-42\right)}{81}=46\)

d: \(=181+3-84+8\cdot25\)

=100+200

=300

e: \(=64\cdot35+140\cdot84-1=2240-1+11760\)

=14000-1

=13999

f: \(=3^3+25\cdot8-1=26+200=226\)

g: \(=3+2^4+1=16+4=20\)

h: \(=36:4\cdot3+2\cdot25-1=27+50-1=27+49=76\)

a,\(5^3.2-100:4+2^3.5\)

= 125 . 2 - 25 + 8 . 5

= 250 - 25 + 40

= 265

b, \(6^2:9+50.2-3^3.3\)

= 36 : 9 + 100 - 27 . 3

= 4 + 100 - 81

= 23

bạn kia ko làm các ý khác à

b) \(5^3\cdot2-100:4+2^3\cdot5\)

\(=125\cdot2-25+8\cdot5\)

\(=250-25+40\)

\(=225+40=265\)

c) \(6^2:9+50\cdot2+3^3-3\)

\(=36:9+100+27-3\)

\(=4+100+27-3\)

\(=104+27-3=131-3=128\)

d) \(3^2\cdot5+2^3\cdot10-81:3\)

\(=9\cdot5+8\cdot10-27\)

\(=45+80-27\)

\(=125-27=98\)

e) \(5^{13}:5^{10}-25\cdot2^2\)

\(=5^{13-10}-5^2\cdot2^2\)

\(=5^3-\left(5\cdot2\right)^2\)

\(=125-10^2\)

\(=125-100=25\)

f) \(20:2^2+5^9:5^8\)

\(=20:4+5^{9-8}\)

\(=5+5^1=5+5=10\)

g) \(100:5^2+7\cdot3^2\)

\(=10^2:5^2+7\cdot9\)

\(=\left(10:5\right)^2+63\)

\(=2^2+63=4+63=67\)

h) \(84:4+3^9:3^7+5^0\)

\(=21+3^{9-7}+1\)

\(=21+3^2+1\)

\(=21+9+1=30+1=31\)

i) \(29-\left[16+3\cdot\left(51-49\right)\right]\)

\(=29-\left[16+3\cdot2\right]\)

\(=29-\left[16+6\right]\)

\(=29-22=7\)

j) \(\left(15^{19}:5^{17}+3\right)\cdot0:7\)

\(=\left[\left(3\cdot5\right)^{19}:5^{17}+3\right]\cdot0\)

Vì số nào nhân cho 0 cũng bằng 0 nên giá trị biểu thức trên bằng 0

k) \(7^9:7^7-3^2+2^3\cdot5\)

\(=7^{9-7}-9+8\cdot5\)

\(=7^2-9+40\)

\(=49-9+40=40+40=80\)

l) \(1200:2+6^2\cdot2^1+18\)

\(=600+36\cdot2+18\)

\(=600+72+18\)

\(=600+\left(72+18\right)=600+90=690\)

m) \(5^9:5^7+70:14-20\)

\(=5^{9-7}+5-20\)

\(=5^2+5-20\)

\(25+5-20=30-20=10\)

Những câu sau mình làm sau nhé bạn!!!!!!!

\(\left(x+1\right)^3=27\)

\(\left(x+1\right)^3=3^3\)

\(\Rightarrow x+1=3\)

\(x=2\)

\(\left(x+1\right)^3=27\)

\(< =>\left(x+1\right)^3=3.3.3=3^3\)

\(< =>x+1=3< =>x=3-1=2\)

\(\left(2x+3\right)^3=9.81\)

\(< =>\left(2x+3\right)^3=9.9.9\)

\(< =>\left(2x+3\right)^3=9^3\)

\(< =>2x+3=9< =>2x=6\)

\(< =>x=\frac{6}{2}=3\)

giúp mình bài này đi

21.73 + 27 . 21

a) Có x = 99 => x+1 = 100

A = x⁵ - (x+1)x⁴ + (x+1)x³ + (x+1)x² + (x+1)x - 9

= x⁵ - x⁵ + x⁴ - x⁴ + x³ - x³ + x² - x² + x - 9

= x - 9

=> A = 90

b) Chữa đề: x⁶ - 20x⁵ - 20x⁴ - 20x³ - 20x² - 20x + 3

Có: x = 21 => x-1 = 20

B = x⁶ - (x-1)x⁵ - (x-1)x⁴ - (x-1)x³ - (x-1)x² - (x-1)x + 3

= x⁶ - x⁶ + x⁵ - x⁵ + x⁴ - x⁴ + x³ - x³ + x² - x + 3

= x + 3

=> B = 24

a;

A = 10⁹ + 10⁸ + 10⁷ 

A = 10^7.(10² + 10 + 1)

A = 10⁶.2.5.(100 + 10 + 1)

A = 10⁶.2.5.111

A = 10⁶.2.555 ⋮ 555 (đpcm)

b;

B = 81⁷ - 27⁹ - 9¹⁹

B = 9¹⁴ - 3⁹.9⁹ - 9¹⁹

B = 9¹⁴ - 3.3⁸.9⁹ - 9¹⁹

B = 9¹⁴ - 3.9⁴.9⁹ - 9¹⁹

B = 9¹⁴ - 3.9¹³ - 9¹⁹

B = 9¹³.(9 - 3 - 9⁶)

B = 9¹³.(9 - 3 - \(\overline{..1}\))

B = 9¹³.(6 - \(\overline{..1}\))

B = 9¹³.\(\overline{..5}\)

B ⋮ 9; B ⋮ 5

B \(\in\) BC(9; 5)  = 9.5 = 45

B ⋮ 45 (đpcm)