a) Ta có:

4³⁰⁰ = (4³)¹⁰⁰ = 64¹⁰⁰

3⁴⁰⁰ = (3⁴)¹⁰⁰ = 81¹⁰⁰

Vì 64¹⁰⁰ < 81¹⁰⁰ nên 4³⁰⁰ < 3⁴⁰⁰

b) Ta có:

8²⁵ = (2³)²⁵ = 2⁷⁵

Vậy 8²⁵ = 2⁷⁵

c) Ta có:

5³⁸ > 5³⁶ = (5³)¹² = 125¹² > 121¹² = (11²)¹² = 11²⁴

Vậy 5³⁸ > 11²⁴

a,

Ta có : \(4^{300}=4^{3\cdot100}=\left(4^3\right)^{100}=64^{100}\)

          \(3^{400}=3^{4\cdot100}=\left(3^4\right)^{100}=81^{100}\)

Vì 64<81 =>\(64^{100}< 81^{100}\) hay \(4^{300}< 3^{400}\)

b, Ta có:

\(2^{75}=2^{3\cdot25}=\left(2^3\right)^{25}=8^{25}\)

Vậy \(2^{75}=8^{25}\)

c,Ta có:

\(5^{36}=5^{3\cdot12}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=11^{2\cdot12}=\left(11^2\right)^{12}=121^{12}\)

Vì 125 >121 =>\(125^{12}>121^{12}\) hay 5³⁶>11²⁴

\(B=\dfrac{864.48-432.96}{864.98.432}\\ =\dfrac{432.2.48-432.2.48}{864.98.432}\\ =\dfrac{0}{864.98.432}\\ =0\)

\(C=\dfrac{7256\times4375-725}{3650+4375\times7255}\\ =\dfrac{\left(7255+1\right)\times4375-725}{3650+4375\times7255}\\ =\dfrac{7255\times4375+4375-725}{3650+4375\times7255}\\ =\dfrac{7255\times4375+3650}{3650+4375\times7255}\\ =1\)

Ta gọi \(A=1+2+2^2+2^3+...+2^{11}\)

      \(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{12}\)

      \(\Rightarrow2A-A=\left(2+2^2+2^3+2^4+...+2^{12}\right)-\left(1+2+2^2+2^3+...+2^{11}\right)\)

      \(\Rightarrow A=2+2^2+2^3+2^4+...+2^{12}-1-2-2^2-2^3-...-2^{11}\)

      \(\Rightarrow A=2^{12}-1\)

      \(\Rightarrow A=4096-1\)

      \(\Rightarrow A=4095\)

\(1+2^4+2^8\)

\(=1+16+256\)

\(=273\)

214 x 72 - 45 x 214 - 214 x 27

= 214 x (72 - 45 - 27)

= 214 x 0

= 0

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

\(3^x=3^{10}\\ =>x=10\)

3^x=3¹⁰

=> x=10

a,\(5^{x-2}-3^2=2^4-\left(2^8.2^4+2^{10}.2^2\right)\)

\(\Leftrightarrow5^{x-2}-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(\Leftrightarrow5^{x-2}-3^2=2^4\)

\(\Leftrightarrow5^{x-2}=2^4+3^2\)

\(5^{x-2}=25\)

\(5^{x-2}=5^2\)

=> x-2 =2 

=> x=4 b,

b,\(697:\left[\left(15.x+264\right):x\right]=17\)

\(\Rightarrow\left(15.x+364\right):x=697:17\)

\(\left(15.x+364\right):x=41\)

\(\Rightarrow15.x+364=41.x\)

\(\Rightarrow15.x-41.x=-364\)

\(-26x=-364\)

=> x= -364 :-26 = 14

c,\(134:\left(x-3\right)=35+160:5\)

\(134:\left(x-3\right)=35+32\)

\(134:\left(x-3\right)=67\)

=> x-3= 134 :67

x- 3 =2

=> x= 5

d,\(\left(3.x-2^4\right).7^3=2.7^4\)

\(3.x-2^4=2.7^4:7^3\)

\(3.x-2^4=2.\left(7^4:7^3\right)\)

\(3.x-2^4=2.7\)

\(3.x-2^4=14\)

\(3.x=14+2^4\)

3x =30

=> x=10

e,\(\left[\left(10-x\right).2+5\right]:3-2=3\)

\(\left[\left(10-x\right).2+5\right]:3=3+2\)

\(\left[\left(10-x\right).2+5\right]:3=5\)

\(\left(10-x\right).2+5=15\)

\(\left(10-x\right).2=10\)

=> 10-x = 5

=> x =10 -5

x =5 

Diện tích mỗi viên gạch là:

\(2400:1500=1.6\left(m^2\right)\)

Độ dài của mỗi viên gạch là:

\(\sqrt{1.6}=\dfrac{2\sqrt{10}}{5}\left(m\right)\)

Vậy mỗi cạnh của viên gạch dài \(\dfrac{2\sqrt{10}}{5}\left(m\right)\)

a, điểm A nằm giữa hai điểm O và B

b, vì A nằm giữa hai điểm O và B nên 

                   OB=OA+AB

               ⇒ AB=OB-OA⇒5-2.5=2.5 (cm)

c, vì OA=2.5 cm nên A là trung điểm của OB

        OB=2.5 cm

O t B A 5 cm 2.5 cm

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