a)  \(2^6.3^3.12^2=2^{2.3}.3^3.12^2=4^3.3^3.12^2=12^3.12^2=12^5\)

b)  \(20^4:2^6=\left(2^2.5\right)^4:2^6=2^8.5^4:2^6=2^2.5^4=2^2.25^2=50^2\)

c) \(100^3:2^5=\left(25.2^2\right)^3:2^5=25^3.2^6:2^5=25^3.2\)

d) \(125^2.9^3.2^6=\left(5^3\right)^2.\left(3^2\right)^3.2^6=5^6.3^6.2^6=30^6\)

e) \(81^4.9^2.3^7= \left(3^4\right)^4.\left(3^2\right)^2.3^7=3^{16}.3^4.3^7=3^{27}\)

g) \(250^6:5^5=\left(2.5^3\right)^6:5^5=2^6.5^{18}:5^6=2^6.5^{12}=50^6\)

1,2⁶.3³.2⁴.3²=2¹⁰.3⁵

2,2⁸.5⁴:2⁶=2².5⁴

3,2².5²:2⁵=\(\frac{1}{2^3}.5^2\)

4,5⁶.9².2⁶=10⁶.9²

5,3¹⁶.3⁴.3⁷=3²⁷

6,5¹⁸.2:5⁵=5¹³.2

\(2^6\cdot3^3\cdot12^2=2^6\cdot3^3\cdot\left(3\cdot2^2\right)^2\)

                           \(=2^6\cdot3^3\cdot3^2\cdot2^4\)

                              \(=2^{10}\cdot3^5\)

\(C=\dfrac{2^6\cdot3^{10}}{3^9\cdot2^6}=3\\ D=\dfrac{3^{24}\cdot3^{10}}{3^{21}\cdot3^{11}}=\dfrac{3^{34}}{3^{32}}=3^2=9\\ F=\dfrac{2^{45}\cdot5^{14}}{5^{15}\cdot2^{47}}=\dfrac{1}{2^2\cdot5}=\dfrac{1}{20}\\ G=\dfrac{2^2\cdot5^2\cdot5^3}{2^3\cdot5^4}=\dfrac{1\cdot5}{2}=\dfrac{5}{2}\)

C=3

D=9

F=1/20

G=5/2

Em ko giải chi tiết vì nó lâu

Mong thông cảm!

C= \(\dfrac{8^2.9^5}{3^9.4^3}\)

   = \(\dfrac{\left(2^3\right)^2.\left(3^2\right)^5}{3^9.\left(2^2\right)^3}\)

   = \(\dfrac{2^6.3^{10}}{3^9.2^6}\)

   = \(\dfrac{3^1}{1}\)

   = \(\dfrac{3}{1}\)

a) 5

b)  − 11 4

c)  2 3

d)  1 100

e) 5

f) 1

a. =(5⁴:5):(5².5)

=5⁵:5³

=5²

b.= (3⁴.3³.3²):(3⁵.3)

=3⁹:3⁶

=3³

d. = 8.125.8.25.8.5.25.2.5

= 2³.5³.2³.5².2³.5.5².2.5

=2¹⁰.5⁹

đúng nha

a; ( 625 : 5) : ( 125 . 5)

 =  ( 5^4 : 5) :  ( 5^3 . 5)

= 5^3 : 5^4

= 1/5

b; (8 1 . 27 . 9 ) : ( 243 . 3)

= ( 3^4 . 3^3 . 3^2) : ( 3^4 . 3)

= 3^9 : 3^ 5

=3^4

c, 1000 x 200 x 40 x 25 

= 1000 x ( 40x 250) x 200

= 1000 x 10000 x 200

= 2000000000

Sửa đề: \(5^9\cdot49^2\)

\(=\dfrac{5^{10}\cdot7^3-5^9\cdot7^4}{5^9\cdot7^3+5^9\cdot14^3}-\dfrac{2^{12}-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}\)

\(=\dfrac{5^9\cdot7^3\left(5-7\right)}{5^9\cdot7^3\left(1+8\right)}-\dfrac{2^{12}\left(1-3^4\right)}{2^{12}\left(3^6+3^5\right)}=\dfrac{-2}{9}+\dfrac{80}{972}\)

=-34/243

\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)

\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)

a) 17.13+17.42-17.35

=17.(13+42-35)

=17.20=340

b) [25.(18-4²)-10]:4+6

=(25.2-10):4+6

=40:4+6=16

c) 3⁶:3²+2³.2²-3².3

=3⁴+2⁵-3³

=81+32-27=86

d) B=3.4²-2².3

=3.(16-4)

=3.12=36

e)2022⁰+3.[5².10-(23-13)²]

=1+3.(250-100)

=1+450=451

g) 27.77+24.27-27

=27.(77+24-1)

=27.100=2700

h) 5.2³+7⁹:7⁷-1²⁰²⁰

=40+7²-1

=89-1=88

i) 120:{54[50:2+(3²-2.4)]}

=120:[54(25+1)]

=120:1404=10/117

Đề bài yêu cầu gì?

a, 4¹⁰. 2³⁰=2²⁰.2³⁰=2⁵⁰

b,9²⁵.27⁴.81³= 3⁵⁰.3¹².3¹²=3⁷⁴

Tương tự các câu khác....

a, 4¹⁰.2³⁰ = (2²)¹⁰.2³⁰ = 2²⁰.2³⁰ = 2⁵⁰
b, 9²⁵.27⁴.81³ = (3²)²⁵.(3³)⁴.(3⁴)³ = 3⁵⁰.3¹².3¹² = 3⁷⁴
c, 25⁵⁰.125⁵ = (5²)⁵⁰.(5³)⁵ = 5¹⁰⁰.5¹⁵ = 5¹¹⁵
d, 64³.4⁸.16⁴ = (2⁶)³.(2²)⁸.(2⁴)⁴ = 2¹⁸.2¹⁶.2¹⁶ = 2⁵⁰
e, 3⁸ : 3⁶ = 3²
2¹⁰ : 8³ = 2¹⁰ : (2³)³ = 2¹⁰ : 2⁹ = 2
12⁷ : 6⁷ = (12 : 6)⁷ = 2⁷
@Dương Tuyết Mai