EXPONENTS AND POWER

 

Worksheet 1

Exponents and Powers  (Class 7 NCERT)

Section A: Fill in the Blanks

1. Section A: Fill in the Blanks

   1. $2^5 \times 2^3 = 2^{\_\_\_}$
      
   2. $(5^3)^2 = 5^{\_\_\_}$
      
   3. Any number raised to the power 0 is equal to ___.
   4. The value of $(-3)^2$ is _____.
   5. Simplify: $\frac{10^5}{10^2} = 10^{\_\_\_}$
      

Section B: Multiple Choice Questions (MCQs)

6. What is the value of $3^{-2}$?

   • a) $\frac{1}{9}$
   • b) $-9$
     
   • c) $9$
     
   • d) $-\frac{1}{9}$​

7. $2^3 \times 3^2 = \_\_\_\_\_$
   

   • a) $36$
     
   • b) $18$
     
   • c) $72$
     
   • d) $108$
     

8. What is the scientific notation of $56000$?

   • a) $5.6 \times 10^4$
     
   • b) $56 \times 10^3$
     
   • c) $5.6 \times 10^3$
     
   • d) $560 \times 10^2$
     

9. Simplify: $\frac{2^6}{2^3}$
   

   • a) $8$
     
   • b) $4$
     
   • c) $2^3$
     
   • d) $6$
     

10. Section C: Short Answer Questions

    11. Write the value of $7^0 + (-4)^0$
        

    12. Simplify: $5^3 \times 2^2 \div 2^3$
        

    13. Write $0.00045$ in scientific notation.

    14. Evaluate: $(-2)^3 + (-2)^2$
        

    15. Express $1.25 \times 10^3$ in standard form.

Section D: Long Answer Questions

16. Simplify and express the answer in exponential form:
    $(3^4 \times 3^2) \div 3^5$
    

17. If $a = 2^3$ and $b = 3^2$ find $a^2 \times b^3$.

18. Write the value of $(2^5)^2$ and compare it with $2^{10}$
    

19. Express $\frac{1}{81}$ as a power of 3.

20. The distance between the Earth and the Moon is approximately $384000$km. Express this distance in scientific notation.

Answer Key

Section A:

1. $8$
2. $6$
3. $1$
4. $9$
5. $3$

Section B:

6. a) $\frac{1}{\mathrm{9}}$
7. c) $72$
   
8. b)5.6 x 10^4
9. a) 8

Section C:

11. $2$
12. $62.5$
13. 4
14. $-4$
15. $1250$
    

Section D:

16. $3$
17. $a^2 \times b^3 = (2^3)^2 \times (3^2)^3 = 2^6 \times 3^6 = (2 \times 3)^6 = 6^6$
    
18. Both are equal.
19. $\frac{1}{81} = 3^{-4}$
    
20. $3.84 \times 10^5$ km

Worksheet 2

Exponents and Powers

Part A: Fill in the Blanks

1. $2^5 =$
2. $3^3 =$
3. The value of $5^0$ is ______.
4. $(10^2)\times (10^3)=\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$
5. $\frac{6^4}{6^2} = \_\_\_\_\_\_$
   

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Part B: True or False

1. $2^3 + 2^3 = 2^6$(True/False)
2. $(3^2)^3 = 3^6$ (True/False)
3. Any non-zero number raised to the power 0 is 0. (True/False)
4. $4^5 \times 4^3 = 4^8$ (True/False)
5. $2^3 \div 2^2 = 2^1$(True/False)

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Part C: Simplify

1. $(2^3)\times (3^2)$
2. $(5^3) \div (5^2)$
   
3. $(7^0)+(2^4)$
4. $(10^3) \div (10^2) \times (10^4)$
   
5. $(2^4)^2$
   

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Part D: Solve

1. Write $81$ as a power of $3$.
2. Express $1000$ as $10^n$.
3. Find the value of $(-3)^3$.
4. Compare $2^5$ and $5^2$.
5. Find $x$ if $2^x = 16$.

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Part E: Word Problems

1. A bacteria doubles every hour. If its initial count is $1$, express its population after:

   • 1 hour
   • 3 hours
   • 6 hours

2. The side of a square is $2^3$ cm. Find its area in exponential form and calculate its value.

3. A machine produces $5^3$ parts in an hour. How many parts will it produce in $2$ hours?

4. Write the standard form of $5 \times 10^3$ and $3.6 \times 10^4$.

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Part F: Match the Following

Expression	Value
$2^4$	16
$(3^2)^2$	81
$5^3 \div 5^2$	5
$10^0$	1
$2^3 + 2^3$	16

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Answer

Part A: Fill in the Blanks

1. $32$
2. $27$
3.  1.
4. 105
5. $36$

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Part B: True or False

1.  False
   
2. True
3.  False
   
4. True
5. True

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Part C: Simplify

1. $2$
2. $5$
3. $17$
4. $100,000$
5. $256$

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Part D: Solve

1. $81 = 3^4$
   
2. $1000 = 10^3$
   
3. $-27$
4.  $2^5 > 5^2$
   
5.  $x = 4$
   

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Part E: Word Problems

1. Bacteria doubling every hour:

   • $2$
   • $8$
   • $64$

2. $\text{side}^2 = (2^3)^2 = 2^{3 \times 2} = 2^6 = 64 \, \text{cm}^2$
   

3. $250$.

4. Standard form:

   • $5000$
   • $36,000$

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Part F: Match the Following

Expression	Value
$2^4$	16
$(3^2)^2$	81
$5^3 \div 5^2$	5
$10^0$	1
$2^3 + 2^3$	16