**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;

- a
^{x}x a^{y}= a^{x+y}

Example – 2^{2}x 2^{4}= 2^{6}= 64 - (a
^{x})^{y}= a^{xy}

Example – (2^{2})^{2}= 2^{4 }= 16 - a
^{x}/a^{y }= a^{x-y}, where x is greater than y

Example – 2^{4}/2^{2}= 2^{2}= 4 - a
^{x}/a^{y}= 1/a^{y-x}, where y is greater than x

Example – 2^{2}/2^{4}= 1/2^{2}= ¼ = 0.25 - (ab)
^{x}= a^{x}b^{x}

Example – (2×3)^{4}= 2^{4}x 3^{4} - (a/b)
^{x}= a^{x}/b^{x}

Example – (⅔)^{5}= 2^{5}/3^{5}

### 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 2 ^{4} + 3^{2}= 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. 3^{6} – 2^{5}

b. 4^{3} + 5^{3}

c. 8^{3 }x 2^{4}

d. 3^{7} ÷ 9^{2}

e. 3^{5} x 4^{7}

f. (5^{3} x 2^{2}) ÷ (5^{2} x 2)

g. (3/2)^{5} x 16 x (2/3)^{4} x 6^{3} 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. 4^{2} x4^{3} / 2^{6}

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. –(5^{2}) 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

**Download Printable Exponents and Powers Worksheet**

**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 (a**^{5}**xb**^{3}**xb**^{6}**) ÷ (a**^{2}**b**^{2}**)**

**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. n^{6}

c. (5^{6})/(5^{4})

**3 **

a. 2^{10}

b. (-2)^{5} X 5^{5}

c. 11^{3}/7^{3}

d. (-⅕)^{3}

**4. **

a. 697

b. 189

c. 2^{13}

d. 3^{3}

e. 3^{5}X 2^{14}

f. 20

g. 2^{9} X 3^{4}

h. 1/(7X5X2^{2})

i. 4

j. 1

k. 2^{4}

l. (-⅓)^{5}

**5. **

a. 3^{6}

b. (-5)^{2}

**6. **

a. 3^{4}X 2^{7}

b. 2^{8} X 11^{2}

**7. **

a. X = 3

b. X = 1

8. A^{3}X B^{7}

**9. **

a. 7.82 X 10^{8}

b. 6.0999 X 10^{2}

c. 2.34 X 10^{4}

d. 5 X 10^{6}

**10.**

a. 9876000

b. 1300000000

11. (6/5)^{6}

**Read related worksheets**

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**Comparing quantities Maths Worksheet Class 7**

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**Sample Paper for Class 7 Maths with Solutions**

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