9:
a: 10^20=(10^2)^10=100^10
100>9
=>100^10>9^10
=>10^20>9^10
b: 6^8=(6^2)^4=36^4
16^12=(16^3)^4=4096^4
mà 36<4096
nên 6^8<16^12
c: \(\left(\dfrac{1}{16}\right)^{10}=\left[\left(\dfrac{1}{2}\right)^4\right]^{10}=\left(\dfrac{1}{2}\right)^{40}>\left(\dfrac{1}{2}\right)^{50}\)
10:
a: \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4\cdot55⋮55\)
b: \(16^5+2^{15}=\left(2^4\right)^5+2^{15}\)
\(=2^{20}+2^{15}=2^{15}\left(2^5+1\right)\)
\(=2^{15}\cdot33⋮33\)
Bài 7:
a) 25 . 5³ . 1/625 . 5²
= 5² . 5³ . 1/5⁴ . 5²
= 5²⁺³⁻⁴⁺²
= 5³
b) 4 . 32 : (2³ . 1/16)
= 2² . 2⁵ : (2³ . 1/2⁴)
= 2² . 2⁵ : 1/2
= 2²⁺⁵⁻¹
= 2⁶
c) (1/7)² . 1/7 . 49²
= 1/7² . 1/7 . (7²)²
= 1/7³ . 7⁴
= 7⁴⁻³
= 7
Bài 6
a) 4².4³/2¹⁰
= 4²⁺³/(2²)⁵
= 4⁵/4⁵
= 1
b) (0,6)⁵/(0,2)⁶
= 0,2⁵.0,3⁵/0,2⁶
= 0,3⁵/0,2
= 243/20000
c) (2⁷.9³)/(6⁵.8²)
=[2⁷.(3²)³]/[2⁵.3⁵.(2³)²]
= (2⁷.3⁶)/(2⁵.3⁵.2⁶)
= (2⁷.3⁶)/(2¹¹.3⁵)
= 3/2⁴
= 3/16
d) (6³ + 3.6² + 3³)/(-13)
= (2³.3³ + 3.2².3² + 3³)/(-13)
= (2³.3³ + 3³.2² + 3³)/(-13)
= 3³.(2³ + 2² + 1)/(-13)
= 3³.13/(-13)
= -3³
= -27
Bài 8
a) (2x - 5)⁴ = -81 (vô lí)
Vậy không tìm được x
b)1/2 . 2ⁿ⁺⁴.2ⁿ = 2⁵
2ⁿ⁺⁴⁺ⁿ⁻¹ = 2⁵
2n + 3 = 5
2n = 5 - 3
2n = 2
n = 2 : 2
n = 1 (nhận)
Vậy n = 1
Bài 5
a) x : (-3/5)² = -3/5
x = -3/5 . (-3/5)²
x = (-3/5)³
x = -27/125
b) (4/7)⁴ . x = (4/7)⁶
x = (4/7)⁶ : (4/7)⁴
x = (4/7)²
x = 16/49
Bài 4
a) (3/7 + 1/2)²
= (13/14)²
= 169/196
b) (3/4 - 4/5)²
= (-1/20)²
= 1/400
c) (5⁴.20⁴)/(25⁵.4⁵)
= (5.20)⁴/(25.4)⁵
= 100⁴/100⁵
= 1/100
d) [(2/3)³.(-3/4)².(-1)²⁰⁰³]/[(2/5)²= .(-5/12)³]
= [8/27 . 9/16 . (-1)]/[4/25 . (-125/1728)]
= (-1/6)/(-5/432)
= 72/5
Bài 3
a) 2.16.8
= 2.2⁴.2³
= 2¹⁺⁴⁺³
= 2⁸
b) 25.5.125
= 5².5.5³
= 5²⁺¹⁺³
= 5⁶
c) 2/3 . 4/9 . 8/27
= 2/3 . (2/3)² . (2/3)³
(2/3)¹⁺²⁺³
= (2/3)⁶
Bài 2
a) (-2/3)³
= (-2)³/3³
= -8/27
b) (-0,1)⁴ = 1/10000
c) [(-2)³]²
= (-2)⁶
= 64
d) [(-1/3)²]³
= (-1/3)⁶
= 1/729
Bài 1
25 = 5²
1/36 = (1/6)²
0,125 = (0,5)³
10000 = 10⁴
25/64 = (5/8)²
27/8 = (3/2)³
