a) Ta có:

\(2^{300}=2^{3\cdot100}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=3^{2\cdot100}=\left(3^2\right)^{100}=9^{100}\)

Mà: \(8< 9\)

\(\Rightarrow8^{100}< 9^{100}\)

\(\Rightarrow2^{300}< 3^{200}\)

b) Ta có:

\(3^{500}=3^{5\cdot100}=\left(3^5\right)^{100}=243^{100}\)

\(7^{300}=7^{3\cdot100}=\left(7^3\right)^{100}=343^{100}\)

Mà: \(243< 343\)

\(\Rightarrow243^{100}< 343^{100}\)

\(\Rightarrow3^{500}< 7^{300}\)

c) Ta có: 

\(8^5=\left(2^3\right)^5=2^{3\cdot5}=2^{15}=2\cdot2^{15}\)

\(3\cdot4^7=3\cdot\left(2^2\right)^7=3\cdot2^{2\cdot7}=3\cdot2^{14}\)

Mà: \(2< 3\)

\(\Rightarrow2\cdot2^{14}< 3\cdot2^{14}\)

\(\Rightarrow8^5< 3\cdot4^7\)

d) Ta có:

\(202^{303}=202^{3\cdot101}=\left(202^3\right)^{101}=8242408^{101}\)

\(303^{202}=303^{2\cdot101}=\left(303^2\right)^{101}=91809^{101}\)

Mà: \(8242408>91809\)

\(\Rightarrow8242408^{101}>91809^{101}\)

\(\Rightarrow202^{303}>303^{202}\)

a) x(x+1)=2+4+6+8+...+2500

x(x+1)=(2500+2).1250:2

x(x+1)=1563750

Ta thấy: x và x+1 là 2 số liên tiếp

Mà x(x+1)=1563750=>x=1250;x+1=1251

Vậy x=1250

b) x-3=12:{390:[500-(5^3+7^2.5)]}

x-3=12:[390:(500-254.64)]

x-3=12:(390:245.35)

x-3=12:1.58

x-3=7.54

=>x=10.5

Vậy x=10.5

c) x+3^3.12=3^3.19

=>x=2.46

Vậy x=2.46

\(7\cdot4^x=112\)

\(\Rightarrow4^x=\dfrac{112}{7}\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

_____
\(2\cdot5^{x-3}=250\)

\(\Rightarrow5^{x-3}=\dfrac{250}{2}\)

\(\Rightarrow5^{x-3}=125\)

\(\Rightarrow5^{x-3}=5^3\)

\(\Rightarrow x-3=3\)

\(\Rightarrow x=3+3\)

\(\Rightarrow x=6\)

____

\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+25\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)

\(=12:\left[400:\left(500-300\right)\right]+10\)

\(=12:\left(400:200\right)+10\)

\(=12:2+10\)

\(=6+10\)

\(=16\)

\(7\cdot4^x=112\)

\(\Rightarrow4^x=112:7\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

Vậy \(x=2.\)

\(---\)

\(2\cdot5^{x-3}=250\)

\(\Rightarrow5^{x-3}=250:2\)

\(\Rightarrow5^{x-3}=125\)

\(\Rightarrow5^{x-3}=5^3\)

\(\Rightarrow x-3=3\)

\(\Rightarrow x=3+3\)

\(\Rightarrow x=6\)

Vậy \(x=6.\)

\(---\)

\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)

\(=12:\left\{400:\left[500-300\right]\right\}+10\)

\(=12:\left\{400:200\right\}+10\)

\(=12:2+10\)

\(=6+10\)

\(=16\)

#\(Toru\)

Câu 1.99²⁰và 9999¹⁰

⁼(99²)¹⁰=9801¹⁰

Vậy 9801¹⁰<9999¹⁰ suy ra  99²⁰<9999¹⁰

Câu 2. 3⁵⁰⁰và 7³⁰⁰

 3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

7³⁰⁰=(7³)¹⁰⁰=343¹⁰⁰

Vậy 243¹⁰⁰<343¹⁰⁰ => 3⁵⁰⁰<7³⁰⁰

Ta có :

3^500= (3^5)^100=15^100

7^300= (7^3)^100=21^100

Vì 15^100 < 21^100 nên 3^500 < 7^300

                       Vậy 3^500 < 7^300

^ có nghĩa là mũ nha

Ta có 3^500= (3^5)^100=243^100

         7^300=(7^3)^100=343^100

Vì 343^100>243^100 nên 3^500<7^300

a) 4.25-12.5+170:10

=100-60+17

=40+17

=57

b) (7+3³:3²).4-3

=(7+3).4-3

=10.4-3

=40-3

=37

c) 12:{400:[500-(125+25.7)]}

=12:{400:[500-(125+175)]}

=12:{400:[500-300]}

=12:{400:200}

=12:2

=6

d) 168+{[2.(2⁴+3²)-256⁰]:7²}

=168+{[2.(16+9)-1]:49}

=168+{[2.25-1]:49}

=168+{[50-1]:49}

=168+{49:49}

=168+1

=169

giúp tôi nha

Ý bạn là:

\(-10^2+\left|-500+3^4\right|\)

\(=100+\left|-500+81\right|\)

\(=100+\left|-419\right|\)

\(=100+419\)

\(=519\)

\(\left(-10\right)^2+\left|-500\right|+3^4=100+500+81\)

\(=681\)