Exponents and Powers Class 7 Maths Worksheet – Chapter 13

Exponents and Powers Class 7 Maths Worksheet – Chapter 13

Exponents and Powers Class 7 – In this worksheet, we have questions from “Exponents and Powers”. This worksheet covers all important concepts from the chapter. It gives you an overall idea and covers all important formulae by applying them. This maths worksheet makes you exam-ready. By attempting this worksheet with time-bound will give you the best preparedness for the exam.

Exponents

What are Exponents? 

 

Exponents reflect the number of times a number is multiplied by itself. For example, 23 means that 2 is multiplied by itself 3 times i.e. 2 x 2 x 2. Therefore, the exponent is the power to which a number is raised. 

 

What are the laws of exponents?

 

Laws of Exponents

 

If a and b are non-zero rational numbers and x and y are natural numbers, then the laws of exponents can be written as;

1. a^x x a^y = a^x+y
   Example – 2²x 2⁴ = 2⁶= 64
2. (a^x)^y = a^xy
   Example – (2²)²= 2⁴ = 16
3. a^x/a^y = a^x-y, where x is greater than y
   Example – 2⁴/2² = 2² = 4
4. a^x/a^y= 1/a^y-x, where y is greater than x
   Example – 2²/2⁴ = 1/2² = ¼ = 0.25
5. (ab)^x = a^x b^x
   Example – (2×3)⁴ = 2⁴ x 3⁴
6. (a/b)^x= a^x/b^x
   Example – (⅔)⁵ = 2⁵/3⁵

 

 

Now that we know about the concept of Exponents and powers, let’s look at the worksheet below to test our understanding. 

Ques 1. Choose the correct option for the following questions – 

 

1. Value of -5 raised to the power of 4 is :

a. -625        

b. 25

c. -125   

d. 625

2. (-1)³¹ equals to:

a. 31

b. -1

c. 1

d. -31

3. What power of -3 is 729?

a. 3

b. 4

c. 6

d. 5

4. Value of (-1)¹⁵ x (-1)¹⁶ equals to;

a. 1

b. -1

c. -240

d. 240

5. If 2⁴ + 3²= 5^x then x equals:

a. 1

b. 2

c. 3

d. 4

Ques 2. Use power notation to express each of the following:

a. ( -2/3) x (-2/3) x(-2/3) x(-2/3)

b. n x n x n x n x n x n

c. (5 x 5 x 5 x 5 x 5 x 5) / (5 x 5 x 5 x 5)

Ques 3. Express each of the following in exponential form:

a. 1024

b. -100000 

c. 1331/343

d. -1/125

 

Ques 4. Evaluate:

a. 3⁶ – 2⁵

b. 4³ + 5³

c. 8³ x 2⁴

d. 3⁷ ÷ 9²

e. 3⁵ x 4⁷

f. (5³ x 2²) ÷ (5² x 2)

g. (3/2)⁵ x 16 x (2/3)⁴ x 6³ x 8

h. (4/7)² x (1/5)² x 35 / 64

i. (1/3)⁴ x (-27/4)² x (-8/3)²

j. [(1/4)³]²÷ [(1/4)²]³

k. 4² x4³ / 2⁶

l. (-1/3)² x (-1/3)³ x (-1/3)⁰

Ques 5. Which of the following is greater:

a. 36 or 63

b. –(5²) or (-5)²

Ques 6. Express each of the following as a product of powers of prime factors:

a. 81 x 128  

b. 256 x 121

 

Ques 7. Find the value of x:

a. {(3)³}⁷ = (3)^7x

b. (-2)¹¹ ÷ (-2)⁹= (-2)^2x

Ques 8. Using laws of exponents simplify (a⁵xb³xb⁶) ÷ (a²b²)

Ques 9. Express the following in standard form:

a. 782000000   

b. 609.99

c. 0.234 x 105   

d. 5 million

Ques 10. Write the following in the usual form:

a. 9.876 x 106

b. 1.3 x 109

Ques 11. Convert the following equation into positive power and then solve – (5/6)^-2/ x (5/6)^-4

Download Printable Exponents and Powers Worksheet Class 7

SOLUTIONS 

 1.

a. D. 625

b. B. -1

c. C. 6

d. B. -1

e. B. 2

2. 

a. (-⅔)⁴

b. n⁶

c. (5⁶)/(5⁴)

3 

a. 2¹⁰

b. (-2)⁵ X 5⁵

c. 11³/7³

d. (-⅕)³

4. 

a. 697

b. 189

c. 2¹³

d. 3³

e. 3⁵X 2¹⁴

f. 20 

g. 2⁹ X 3⁴

h. 1/(7X5X2²)

i. 4

j. 1

k. 2⁴

l. (-⅓)⁵

5. 

 a. 3⁶

b. (-5)²

6. 

a. 3⁴X 2⁷

b. 2⁸ X 11²

7. 

a. X = 3

b. X = 1

8.  A³X B⁷

9.  

a. 7.82 X 10⁸

b. 6.0999 X 10²

c. 2.34 X 10⁴

d. 5 X 10⁶

10.

a. 9876000

b. 1300000000

11.  (6/5)⁶

 

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Sample Paper for Class 7 Maths with Solutions

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