a. \(12^2.3^2.2^3=2^4.3^2.3^2.2^3=2^7.3^4\)

b. \(8^3.3^2.6^3=2^9.3^2.2^3.3^3=2^{12}.3^5\)

c. \(5^{32}.5^2=5^{34}\)

d. \(100^6.2^3=\left(2^2.5^2\right)^6.2^3=2^8.5^8.2^3=2^{11}.5^8\)

e. \(100^2:10^2:5^2=\left(10.5.2\right)^2:10^2:5^2=2^2\)

f. \(121^3-11^2=11^6-11^2=11^2\left(11^4-1\right)\)

cho mình hỏi mũ là gì

= 81

d, D = 40² - 28² + 32² +80.32

    D = (40² + 2.40.32 + 32²) - 28²

    D = (40 + 32)² - 28²

    D = (40 + 32 - 28)(40 + 32 + 28)

    D = 44.100

   D = 4400

  e, E = 10.80,5 + 10.19,5 - 8.20,5 - 8. 79,5

      E =  10.(80,5 + 19,5) - 8.( 20,5 + 79,5)

      E = 10.100 - 8.100

     E = 100.(10-8)

     E = 200

F = 50² - 18² + 32² + 100.32

F = (50² - 18²) + 32.( 32 + 100)

F = (50 -18)(50+18) + 32. 132

F = 32.68 + 32.132

F = 32.( 68 + 132)

F = 32. 200

F = 6400

a: \(\frac{4^5\cdot10\cdot5^6+25^5\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}\)

\(=\frac{2^{10}\cdot2\cdot5\cdot5^6+5^{10}\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}=\frac{2^8\cdot5^7\left(2^3+3^3\right)}{2^5\cdot5^4\left(2^3+3^3\right)}\)

\(=2^3\cdot5^3=10^3=1000\)

b: \(149-\left(35:x+3\right)\cdot17=13\)

=>\(\left(35:x+3\right)\cdot17=149-13=136\)

=>35:x+3=136:17=8

=>35:x=8-3=5

=>\(x=\frac{35}{5}=7\)

c: \(121:11-\left(4x+5:3\right)=4\)

=>11-(4x+5/3)=4

=>4x+5/3=11-4=7

=>\(4x=7-\frac53=\frac{21}{3}-\frac53=\frac{16}{3}\)

=>\(x=\frac{16}{3}:4=\frac43\)

d: \(720:\left\lbrack41-\left(2x-5\right)\right\rbrack=40\)

=>\(41-\left(2x-5\right)=\frac{720}{40}=18\)

=>2x-5=41-18=23

=>2x=28

=>\(x=\frac{28}{2}=14\)

e: Sửa đề: (x+1)+(x+2)+(x+3)+...+(x+100)=5700

=>100x+(1+2+3+...+100)=5700

=>\(100x+100\cdot\frac{101}{2}=5700\)

=>x+50,5=57

=>x=57-50,5

=>x=6,5

Bài 1: a)  \(M=1+5+5^2+...+5^{100}\)

\(5M=5+5^2+5^3+...+5^{101}\)

\(5M-M=\left(5+5^2+5^3+...+5^{101}\right)-\left(1+5+5^2+...+5^{100}\right)\)

\(4M=5^{101}-1\)

\(M=\frac{5^{101}-1}{4}\)

b) \(N=2+2^2+...+2^{100}\)

\(2N=2^2+2^3+...+2^{101}\)

\(2N-N=\left(2^2+2^3+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)\)

\(N=2^{101}-2\)

Bài 2:

a) \(16^{32}=\left(2^4\right)^{32}=2^{128}\) 

\(32^{16}=\left(2^5\right)^{16}=2^{80}\)

Vì \(2^{128}>2^{80}\Rightarrow16^{32}>32^{16}\)

(1981 x 1982 - 990) : (1980 x 1982 + 992)

=(1980 x 1982+1982 -990) : (1980 x 1982 +992)

=(1980 x 1982 + 992) : ( 1980 x 1982 + 992)

=1

B=[(45.79+45.21)]:90-5^2]:5+2^3                                  B=[(45.79+45.21):90-25]:5+8                                      B=[(45.(79+21):65]:13                                                  B=[(45.100):65]:13                                                        B=[4500:65]:13                                                           B=4500:65:13                                                       

bạn ơi ARMY ko viết tên như kia đâu