b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)

6:=(3/2)*(3/2)^2*(3/2)^4=(3/2)^7

7: =(1/2)^7*2^3*2^5*2^8=2^9

8: =(-1/7)^4*5^4=(-5/7)^4

9: =2^2*2^5:(2^3/2^4)

=2^7/2=2^6

10: =(1/7)^3*7^2=1/7

a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)

b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)

c: \(16\cdot81=36^2\)

d: \(25^4\cdot2^8=100^4\)

1) a) 4⁸.2²⁰ = (2²)⁸.2²⁰

= 2¹⁶.2²⁰ = 2³⁶

-----------

9¹².27⁵.81³ = (3²)¹².(3³)⁵.(3⁴)⁴

= 3²⁴.3¹⁵.3¹⁶ = 3⁵⁵

--------

64³.4⁵.16² = (4³)³.4⁵.(4²)²

= 4⁹.4⁵.4⁴ = 4¹⁸

b) 25²⁰.125⁴ = (5²)²⁰.(5³)⁴

= 5⁴⁰.5¹² = 5⁵²

--------

x⁷.x³.x⁴ = x¹⁴

--------

3⁶.4⁶ = (3.4)⁶ = 12⁶

2) a) 2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

2⁶ = 64

2⁷ = 128

2⁸ = 256

2⁹ = 512

2¹⁰ = 1024

b) 3² = 9

3³ = 27

3⁴ = 81

3⁵ = 243

c) 4² = 16

4³ = 64

4⁴ = 256

d) 5² = 25

5³ = 125

5⁴ = 625

3)

a) 4⁹ : 4⁴ = 4⁵

17⁸ : 17⁵ = 17³

2¹⁰ : 8² = 2¹⁰ : (2³)² = 2¹⁰ : 2⁶ = 2⁴

18¹⁰ : 3¹⁰ = (18 : 3)¹⁰ = 6¹⁰

27⁵ : 81³ = (3³)⁵ : (3⁴)³ = 3¹⁵ : 3¹² = 3³

b) 10⁶ : 100 = 10⁶ : 10² = 10⁴

5⁹ : 25³ = 5⁹ : (5²)³ = 5⁹ : 5⁶ = 5³

4¹⁰ : 64³ = 4¹⁰ : (4³)³ = 4¹⁰ : 4⁹ = 4

2²⁵ : 32⁴ = 2²⁵ : (2⁵)⁴ = 2²⁵ : 2²⁰ = 2⁵

18⁴ : 9⁴ = (18 : 9)⁴ = 2⁴

\(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)

\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8=\left(\dfrac{1}{7}\right)^7\times2^{16}\)

\(\left(-\dfrac{1}{7}\right)^4\times125\times5=\left(-\dfrac{1}{7}\right)^4\times5^3\times5=\left(-\dfrac{1}{7}\right)^4\times5^4\)

\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:2^3:2^{-4}=2^0\)

\(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^3\times7^3=1^3\)
 

6, \(\dfrac{3}{2}\times\dfrac{9}{4}\times\dfrac{81}{16}=\dfrac{3}{2}\times\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^4\)

7,\(\left(\dfrac{1}{2}\right)^7\times8\times32\times2^8=\left(\dfrac{1}{2}\right)^7\times2^3\times2^5\times2^8\)

8,\(\left(-\dfrac{1}{7}\right) ^4\times125\times5=\left(\dfrac{1}{7}\right)^4\times5^3\times5\)

9,\(4\times32:\left(2^3\times\dfrac{1}{16}\right)=2^2\times2^5:\left[2^3\times\left(\dfrac{1}{2}\right)^4\right]\)

10, \(\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times49=\left(\dfrac{1}{7}\right)^2\times\dfrac{1}{7}\times7^2\)

6) \(...=\dfrac{3}{2}.\left(\dfrac{3}{2}\right)^2.\left(\dfrac{3}{2}\right)^4=\left(\dfrac{3}{2}\right)^7\)

7) \(...=2^{-7}.2^3.2^5.2^8=2^9\)

8) \(...=\left(\dfrac{1}{7}\right)^4.5^3.5=\left(\dfrac{1}{7}\right)^4.5^4\)

9) \(...=2^2.2^5:\left(2^3.2^{-4}\right)=2^8\)

10) \(...=\left(\dfrac{1}{7}\right)^3.\left(\dfrac{1}{7}\right)^2=\left(\dfrac{1}{7}\right)^5\)

a, 4⁸.8⁴

= (2²)⁸.(2³)⁴

= 2¹⁶.2¹²

= 2²⁸

b, 4¹⁵.5¹⁵

= (4.5)¹⁵

= 20¹⁵

c, 2¹⁰.15 + 2¹⁰.85

= 2¹⁰.(15 + 85)

= 2¹⁰.100

=2¹⁰.(2.5)²

= 2¹².5²

d, 3³.9²

= 3³ . (3²)²

= 3³.3⁴

= 3⁷

e, 5¹².7 - 5¹¹.10

= 5¹¹.(5.7 - 10)

= 5¹¹.25

=5¹¹.5²

=5¹³

f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)

= \(x^{1+2+3+...+100}\)

= \(x^{\left(1+100\right).100:2}\)

= \(x^{5050}\)

❤Em cảm ơn cô Nguyễn Thương hoài rất nhiều a!❤

a, 48.84

= (22)8.(23)4

= 216.212

= 228

b, 415.515

= (4.5)15

= 2015

c, 210.15 + 210.85

= 210.(15 + 85)

= 210.100

=210.(2.5)2

= 212.52

d, 33.92

= 33 . (32)2

= 33.34

= 37

e, 512.7 - 511.10

= 511.(5.7 - 10)

= 511.25

=511.52

=513

f, �1x1.�2x2.�3x3....�100x100

= �1+2+3+...+100x1+2+3+...+100

= �(1+100).100:2x(1+100).100:2

= �5050x5050

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