Bài 7: Lũy thừa với số mũ tự nhiên. Nhân hai lũy thừa cùng cơ số. Luyện tập

\(A=8^2\cdot324=8^2\cdot18^2=144^2=\left(12^2\right)^2=12^4\)

\(B=27^3\cdot9^4\cdot243=\left(3^3\right)^3\cdot\left(3^2\right)^4\cdot3^5=3^9\cdot3^8\cdot3^5=3^{22}\)

\(C=6^2\cdot36^4\cdot216^2=6^2\cdot\left(6^2\right)^4\cdot\left(6^3\right)^2=6^2\cdot6^8\cdot6^6=6^{16}\)

\(D=3^4\cdot81^2\cdot9^5=3^4\cdot\left(3^4\right)^2\cdot\left(3^2\right)^5=3^4\cdot3^8\cdot3^{10}=3^{22}\)

GẤP Ạ!!!!!!!!!!!!

2^91 > 2^90

2^90=(2^5)^18=32^18

5^35<5^36

5^36=(5^2)^18=25^18

25^18<32^18

=>2^90 > 5^36

=>2^91>2^90>5^36>5^35

=>2^91>5^35

107^50<108^50

108^50=(4.27)^50=4^50 . 27^50=2^100 . 3^150

73^75>72^75

72^75=(8.9)^75=8^75 . 9^75 = 2^225 . 3^150

Vì 2^225>2^100

=>108^50<72^75
=>107^50<108^50<72^75<73^75

=>107^50<73^75

\(10^{10}=2^{10}\cdot5^{10}\)

\(48\cdot50^5=2^4\cdot3\cdot2^5\cdot5^{10}\)

\(=2^9\cdot3\cdot5^{10}\)

2^10=2^9*2<2^9*3

=>\(2^{10}\cdot5^{10}< 2^9\cdot3\cdot5^{10}\)

=>\(10^{10}< 48\cdot50^5\)

\(11^{1979}< 11^{1980}=\left(11^3\right)^{660}=1331^{660}\)

\(37^{1320}=\left(37^2\right)^{660}=1369^{660}\)

1331<1369

=>\(1331^{660}< 1369^{660}\)

=>\(11^{1980}< 37^{1320}\)

=>\(11^{1979}< 37^{1320}\)

\(99^{20}=\left(99^2\right)^{10}=9801^{10}\)

Do 9801 < 9999 

⇒ 9801¹⁰ < 9999¹⁰.

1: =>\(5^{x-2}-9=2^4-\left(6^2-6^2\right)\)

=>\(5^{x-2}=16+9=25\)

=>x-2=2

=>x=4

2: \(\Leftrightarrow3^x+16=19^6:19^5-3=19-3=16\)

=>3^x=0

=>x=0

3: \(\Leftrightarrow2^x+2^x\cdot16=272\)

=>2^x*17=272

=>2^x=16

=>x=4

4: \(\Leftrightarrow2^{x-1}+3=24-\left(4^2-2^2+1\right)=24-\left(16-4+1\right)\)

=>\(2^{x-1}+3=24-16+4-1=8+4-1=12-1=11\)

=>2^x-1=8

=>x-1=3

=>x=4

a: 6*6*6*6*6=6^5

b: 25*25*25*5=5^2*5^2*5^2*5=5^7

c: 8*2*2*16*4

=2^3*2^2*2^4*2^2

=2^11

d: \(3\cdot3\cdot3\cdot15\cdot5\cdot5\cdot5=15\cdot15\cdot15\cdot15=15^4\)

1: \(\Leftrightarrow\left(x-1\right)^x\cdot\left(x-1\right)^2-\left(x-1\right)^x=0\)

=>\(\left(x-1\right)^x\cdot\left[\left(x-1\right)^2-1\right]=0\)

=>\(x\left(x-1-1\right)\cdot\left(x-1\right)^x=0\)

=>x(x-2)(x-1)^x=0

=>x=0;x=2;x=1

2: \(\Leftrightarrow\left(6-x\right)^{2003}\left(x-1\right)=0\)

=>6-x=0 hoặc x-1=0

=>x=6;x=1

3: =>(7x-11)^3=32*25+200=1000

=>7x-11=10

=>7x=21

=>x=3

4: =>x^2-1=-3 hoặc x^2-1=3

=>x^2=-2(loại) hoặc x^2=4

=>x=2 hoặc x=-2

a: =>2x^3=58-4=54

=>x^3=27

=>x=3

b; =>(5-x)^5=2^5

=>5-x=2

=>x=3

c: =>(5x-6)^3=4^3

=>5x-6=4

=>5x=10

=>x=2

d: (3x)^3=(2x+1)^3

=>3x=2x+1

=>x=1

1=>2x³=54
=>x³=27  =>x=3
2=>(5-x)⁵=2⁵
=>5-x=2
=>x=3
3=>(5x-6)³=4³
=>5x-6=4
=>5x=10=>x=2
4=>3x=2x+1
=>x=1