Find the value of:

1. 2⁶           

2. 9³             

3. 11²              

4. 5⁴

Express the following in exponential form:

1. 6 × 6 × 6 × 6

2. t × t  

3. b × b × b × b

4. 5 × 5 × 7 × 7 × 7

5. 2 × 2 × a × a

6. a × a × a × c × c × c × c × d

Express each of the following numbers using exponential notations:

1. 512         

2. 343           

3. 729            

4. 3125

Identify the greater number, wherever possible, in each of the following:

1. 4³ and 3⁴      

2. 5³ or 3⁵    

3. 2⁸ or 8²    

4. 100² or 2¹⁰⁰      

5. 2¹⁰ or 10²

 

Express each of the following as product of powers of their prime factors:

1. 648         

2. 405          

3. 540          

4. 3,600

Simplify:

1. 2 × 10³          

2. 7² × 2²            

3. 2³ × 5           

4. 3 × 4⁴                

5. 0 × 10²

6. 5² × 3³             

7. 2⁴ × 3²      

8. 3² × 10⁴

Simplify:

1. (-4)³         

2. (-3) × (-2)³          

3. (-3)² × (-5)²          

4. (-2)³ × (-10)³

Compare the following numbers:

1. 2.7 × 10¹²; 1.5 × 10⁸              

2. 4 × 10¹⁴; 3 × 10¹⁷

 

Using laws of exponents, simplify and write the answer in exponential form:

1. 3² × 3⁴ × 3⁸              

2. 6¹⁵ ÷ 6¹⁰               

3. a³ × a²            

4. 7^x × 7²         

5. (5²)³ ÷ 5³             

6. 2⁵ × 5⁵                  

7. a⁴ × b⁴               

8. (3⁴)³             

9. (2²⁰ ÷ 2¹⁵) × 2³       

10. 8^t ÷ 8²

Simplify and express each of the following in exponential form:

1. (2³ × 3⁴ × 4) ÷ (3 × 32)         

2. [(5²)³ × 5⁴] ÷ 5⁷        

3. 25⁴ ÷ 5³           

4. (3 × 7² × 11⁸) ÷ (21 × 11³)

5. 3⁷ ÷ (3⁴ × 3³)     

6. 2⁰ + 3⁰ + 4⁰    

7. 2⁰ × 3⁰ × 4⁰  

8. (3⁰ + 2⁰) × 5⁰   

9. (2⁸ × a⁵) ÷ (4³ × a³)   

10. (a⁵ ÷ a³) × a⁸        

11. (4⁵ × a⁸ b³) ÷ (4⁵ × a⁵ b²)   

12. (2³ × 2)²

Say true or false and justify your answer:

1. 10 × 10¹¹ = 100¹¹      

2. 2³ > 5²       

3. 2³ × 3² = 6⁵       

4. 3⁰ = (1000)⁰

Express each of the following as a product of prime factors only in exponential form:

1. 108 × 192       

2. 270        

3. 729 × 64        

4. 768

Simplify:

1. {(2⁵)² × 7³} ÷ (8³ × 7)        

2. (25 × 5² × t⁸) ÷ (10³ × t⁴)        

3. (3⁵ × 10⁵ × 25) ÷ (5⁷ × 6⁵)

Write the following numbers in the expanded form:

279404, 3006194, 2806196, 120719, 20068

Find the number from each of the following expanded forms:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(c) 3 × 10⁴ + 7 × 10² + 5 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

Express the following numbers in standard form:

1. 5,00,00,000         

2. 70,00,000             

3. 3,18,65,00,000           

4. 3,90,878

5. 39087.8           

5. 3908.78

Express the number appearing in the following statements in standard form:

(a) The distance between Earth and Moon is 384,000,000 m.

(b) Speed of light in vacuum is 300,000,000 m per s.

(c) Diameter of Earth id 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are on an average 100,000,000,0000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be

300,000,000,000,000,000,000 m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The Earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in march, 2001.