a) \(2^3\cdot4^5=2^3\cdot2^{10}=2^{13}\)

b) \(3^4\cdot27^2=3^4\cdot3^6=3^{10}\)

c) \(16^{10}:8^2=2^{40}:2^6=2^{34}\)

d) \(12^3:3^3=\left(12:3\right)^3=4^3\)

e) \(3^4\cdot2^4=\left(3\cdot2\right)^4=6^4\)

g) \(9^{13}\cdot5^{26}=9^{13}\cdot25^{13}=\left(9\cdot25\right)^{13}=225^{13}\)

=))

a) \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)

b) \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)

c) \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)

d) \(x^2=x^3\Rightarrow x^3-x^2=0\Rightarrow x^2\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

e) \(3^{x-1}=27\Rightarrow3^{x-1}=3^3\Rightarrow x-1=3\Rightarrow x=4\)

f) \(3^{x+1}=9\Rightarrow3^{x+1}=3^2\Rightarrow x+1=2\Rightarrow x=1\)

g) \(6^{x+1}=36\Rightarrow6^{x+1}=6^2\Rightarrow x+1=2\Rightarrow x=1\)

h) \(3^{2x+1}=27\Rightarrow3^{2x+1}=3^3\Rightarrow2x+1=3\Rightarrow2x=2\Rightarrow x=1\)

i) \(x^{50}=x\Rightarrow x^{50}-x=0\Rightarrow x\left(x^{49}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1=1^{49}\end{matrix}\right.\)  \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

4ⁿ  =  4096 

4ⁿ = 2¹²

n = 12

5ⁿ = 15625 

5ⁿ = 5⁶

n   = 6

6ⁿ⁺³ = 216

6ⁿ⁺³ = 2³.3³

6ⁿ⁺³ = 6³

n + 3 = 3

4ⁿ = 4096

4ⁿ = 4⁶

n = 6 (nhận)

Vậy n = 6

--------------------

5ⁿ = 15625

5ⁿ = 5⁶

n = 6 (nhận)

Vậy n = 6

--------------------

4ⁿ⁻¹ = 1024

4ⁿ⁻¹ = 4⁵

n - 1 = 5

n = 6 (nhận)

Vậy n = 6

-------------------

6ⁿ⁺³ = 216

6ⁿ⁺³ = 6³

n + 3 = 3

n = 0  (nhận)

Vậy n = 0

--------------------

x² = x³

x³ - x² = 0

x(x² - 1) = 0

x = 0 (nhận) hoặc x² - 1 = 0

*) x² - 1 = 0

x² = 1

x = 1 (nhận) hoặc x = -1 (loại)

Vậy x = 0; x = 1 

--------------------

3ˣ⁻¹ = 27

3ˣ⁻¹ = 3³

x - 1 = 3

x = 3 + 1

x = 4 (nhận)

Vậy x = 4

---------------------

3ˣ⁺¹ = 9

3ˣ⁺¹ = 3²

x + 1 = 2

x = 2 - 1

x = 1 (nhận)

Vậy x = 1

--------------------

6ˣ⁺¹ = 36

6ˣ⁺¹ = 6²

x + 1 = 2

x = 2 - 1

x = 1 (nhận)

Vậy x = 1

--------------------

3²ˣ⁺¹ = 27

3²ˣ⁺¹ = 3³

2x + 1 = 3

2x = 3 - 1

2x = 2

x = 1 (nhận)

Vậy x = 1

--------------------

x⁵⁰ = x

x⁵⁰ - x = 0

x(x⁴⁹ - 1) = 0

x = 0 (nhận) hoặc x⁴⁹ - 1 = 0

*) x⁴⁹ - 1 = 0

x⁴⁹ = 1

x = 1 (nhận)

Vậy x = 0; x = 1

a) 2 mũ 6 nhân 125 mũ 2 = 1000000 ( 1 triệu )

b) 27 mũ 4 chia 3 mũ 8 = 81

c) 18 mũ 8 nhân 9 mũ 4 = 7.2301961e+13 ( tính được nhưng dài )

d) 4 mũ 9 chia 5 mũ 27 = 3.5184372e-14 ( tính được nhưng dài )

a. 2⁶ . 125²

= (2³)² . 125²

= 8² . 125²

= (8.125)² = 1000²

b. 27⁴ : 3⁸

= (3³)⁴ : 3⁸

= 3¹² : 3⁸

= 3^12-8 = 3⁴

c. 18⁸ . 9⁴

= 18⁸ . (3²)⁴

= 18⁸ . 3⁸

= (18.3)⁸ = 54⁸

d. 4⁹ : 5²⁷

= 4⁹ : (5³)⁹

= 4⁹ : 125⁹

= (4 : 125)⁹ = (0,032)⁹

a)     2⁶.125²= 1000000

  b)    27⁴:3⁸  = 81

a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)

 1/2 x 2 mũ n cộng 4 x 2 mũ n = 9 x 2 mũ n

a) (4 * 5)^13 = 20^13 b) (27^16) / (9^10) = 3^(3*16) / 3^(2*10) = 3^48 / 3^20 c) (16^3) / (8^4) = 2^(4*3) / 2^(3*4) = 2^12 / 2^12 = 1

65536

387420489

33554432

536870912

390625

6561

2⁴ . 2⁶ . 2 = 2¹¹

3⁵ . 27 . 81 . 3⁶ = 3⁵ . 3³ . 3⁴ . 3⁶ = 3¹⁸

4² . 4¹⁵ . 64 = 4² . 4¹⁵ . 4³ = 4²⁰

2⁹ . 16 . 4⁸ = 2⁹ . 2⁴ . (2²)⁸ = 2⁹ . 2⁴ . 2¹⁶ = 2²⁹

5¹² : 5⁴ = 5⁸

27⁴ : 3⁴ = (27:3)⁴ = 9⁴

$a,$

$2^{20}.15+2^{10}.85$

$=2^{20}.2^{10}.85+15$

$=2^{30}.100$

$=2^{30}{.10}^2$    

$b,$

${27}^{16}:9^{10}$

$=(3^3{)}^{16}:(3^2{)}^{1}0$

$=3^{48}:3^{20}$

$=3^{28}$ 

$c,$ 

${125}^3:{25}^4$

$=(5^3{)}^5:(5^2{)}^4$

$=5^{15}:5^8$

$=5^7$

$d,$

${24}^4:3^4-{32}^{12}:{16}^{12}$

$=(24:3{)}^4-(32:16{)}^{12}$

$=8^4-2^{12}$

$=(2^3{)}^4-2^{12}$

$=2^{12}-2^{12}$ 

câu 1 : điền dấu > , < , = thích hợp

\(a,0>\left(-25\right).\left(-19\right).\left(-1\right)^{2n}\)

\(b,\left(-3\right)^4.\left(-19\right)^2=3^4.19^2.\left(-1\right)^{100}\)

\(c,\left(-2006\right).9\left(-2007\right)>\left(-2008\right).2009\)

câu 2 : sắp xếp các số theo thứ tự tăng dần

- 37 ; 25 ; 0 ; dấu giá trị tuyệt đối nha / -18 / ;  _ (-19 ) ; _ / - 39 / ; _ ( + 151 )

Có : \(-37;25;0;18;19;-39;-151\)

Thứ tự tăng dần : \(-151;-39;-37;25;19;18;0\)

câu 3 tính

\(\text{a ) -8 + 19}=11\)

\(\text{b ) ( -27 ) : ( -3 )}=9\)

c )\(4-\left(-13\right)=17\)

d )\(\text{ - 9 -13 -( -24 ) + 11=13}\)

\(e,323-6\left[3-7.\left(-9\right)\right]=-73\)

\(f,\left(-3\right)^5.\left(-3\right)^3-9\)\(=6552\)

\(g,9-8.16-13.8\)

\(=9-8.\left(16-13\right)\)

\(=9-8.4\)

\(=9-32\)

\(=-23\)

\(h,\left(-3\right)^2+\left\{-54:\left[\left(-2\right)^3+7.|-2|\right].\left(-2\right)^2\right\}\)

\(=9+\left\{-54:\left[\left(-8\right)+7.2\right].4\right\}\)

\(=9+\left\{-54:\left[\left(-8\right)+14\right].4\right\}\)

\(=9+\left\{-54:6.4\right\}\)

\(=9+\left\{-7.4\right\}\)

\(=9+\left(-28\right)\)

\(=-19\)

học tốt

A=5^10 .9+5^10.7 / 5^9.2^4

A=5^10.(9+7) / 5^9.16

A=5^10.16 /5^9.16

A=5^9.5.16/5^9.16

=>A=5/1

=>A=1

B=2^10.55+2^10. 26 / 2^8 . 27

B=2^10.(55+26) / 2^8 .27

B=2^10.81 / 2^8 .27

B=2^8.2^2.81 / 2^8.27

=>B=2^2.81 / 27

=>B=4.81 / 27

=>B=4.3^3.3 / 3^3

=>B=4.3

=>B=12

Cn phần C thì....mik chưa rõ lém nhưng mak nếu ai cko mik là dzui lém òy......ủng hộ nhoa mina

6 nhaan3 băng2