4 6 .   9 5 +   6 9 .   120 8 4 .   3 12 − 6 11 = 2 2 6 . 3 2 5 + 2 9 .3 9 .2 3 .3.5 2 3 4 .3 12 − 2 11 .3 11 = 2 12 .3 10 + 2 12 .3 10 .5 2 12 .3 12 − 2 11 .3 11 = 2 12 .3 10 1 + 5 2 11 .3 11 2.3 − 1 = 2.6 3.5 = 4 5

Sửa đề: 4^10

\(\dfrac{4^{10}\cdot9^3-6^9\cdot120}{8^4\cdot3^{12}+6^{11}}\)

\(=\dfrac{2^{20}\cdot3^6-2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^6\left(2^8-3^4\cdot5\right)}{2^{11}\cdot3^{11}\left(2\cdot3+1\right)}=\dfrac{2}{3^5}\cdot\dfrac{-149}{7}=\dfrac{-298}{3^5\cdot7}\)

a: \(3^2\cdot\frac{1}{243}\cdot81^2\cdot\frac{1}{3^2}\)

\(=\frac{3^2}{3^5}\cdot\frac{3^8}{3^2}=\frac{1}{3^3}\cdot3^6=3^3=27\)

b: \(4^6\cdot256^2\cdot2^4=\left(2^2\right)^6\cdot\left(2^8\right)^2\cdot2^4\)

\(=2^{12}\cdot2^{16}\cdot2^4=2^{12}\cdot2^{20}=2^{32}\)

c: \(4^6\cdot9^5+6^9\cdot120\)

\(=2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5\)

\(=2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5\)

\(=2^{12}\cdot3^{10}\cdot6=2^{13}\cdot3^{11}\)

Ta có \(8^4\cdot3^{12}-6^{11}\)

\(=2^{12}\cdot3^{12}-2^{11}\cdot3^{11}\)

\(=2^{11}\cdot3^{11}\left(2\cdot3-1\right)=2^{11}\cdot3^{11}\cdot5\)

Ta có: \(A=\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

\(=\frac{2^{13}\cdot3^{11}}{2^{11}\cdot3^{11}\cdot5}=\frac{2^2}{5}=\frac45\)

d: \(4^2\cdot25^2+32\cdot125\)

\(=2^4\cdot5^4+2^5\cdot5^3\)

\(=2^4\cdot5^3\left(5+2\right)=2^4\cdot5^3\cdot7\)

\(B=\frac{4^2\cdot25^2+32\cdot125}{2^3\cdot5^2}\)

\(=\frac{2^4\cdot5^3\cdot7}{2^3\cdot5^2}=2\cdot5\cdot7=70\)

b:\(1+2+3+...+n=\dfrac{n\left(n+1\right)}{2}\)

c: \(1+3+5+...+37\)

Số số hạng là:

(37-1):2+1=19(số)

Tổng là: \(\dfrac{38\cdot19}{2}=19\cdot19=361\)

73 x 46 + 27 x 46 = 46 x [ 73 +27 ] = 46 x 100 = 4600

84 x 312 + 18x 312 = 312 x[84+18]=312x 102 = 31824

15 x5 + 15 x6 -15 + 100 =150

DT hồ đó là

378x[378x3]= 428652 m vuông

Đ/S : 428652m vuông

73 x 46 + 27 x 46

= ( 73 + 27 ) x 46

= 100 x 46

= 4600

84 x 312 + 18 x 312 

= ( 84 + 18 ) x 312 

= 102 x 312

= 31824

15 x 5 + 15 x 6 - 15 + 100

= 15x ( 5 + 6 - 1 ) + 100

= 15 x 10 - 100

= 150 - 100

= 50

x : [ 9 x 6 ] = 4

x : 54 = 4

     x  = 4 x 54

     x = 216

Bài 2 :

Chiều dài khu rừng là :

378 x 3 = 1134 ( m )

Diện tích khu rừng là :

378 x 1134 = 428652 (m2 )

Đáp số : 428652 m2

\(\dfrac{24}{600}=\dfrac{1}{25}\)

\(\dfrac{95}{500}=\dfrac{19}{100}\\ \dfrac{12}{400}=\dfrac{3}{100}\\ \dfrac{84}{200}=\dfrac{21}{50}\)

24/600 = 4/100 

95/500 = 19/100

12/400 = 3/100

750/600 = 125/100

84/200 = 42/100

12=2².3
15=3.5
21=3.7
32=25
46=2.23
98=2.7²

120=2³.3.5
127=127(nó nguyên tố)
214=2.107
275=5².11
312=2³.3.13

450=2.3².5²
900=2².3².5²

giải chi tiết nha mn