Exponents and Powers Class 8 Worksheet

Exponents and powers help us write repeated multiplication in a short form.

Example:

$2^4 = 2 \times 2 \times 2 \times 2 = 16$24=2×2×2×2=16

Here, 2 is the base and 4 is the exponent.

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Important Laws of Exponents

1. Product Law

$a^m \times a^n = a^{m+n}$am×an=am+n

2. Quotient Law

$\frac{a^m}{a^n} = a^{m-n}$anam​=am−n

3. Power of a Power

$(a^m)^n = a^{mn}$(am)n=amn

4. Zero Exponent Rule

$a^0 = 1$a0=1

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Section A – Fill in the Blanks

1. $5^2$52 = ________
2. $10^3$103 = ________
3. $2^5$25 = ________
4. Any number raised to power 0 is ________.
5. $3^4$34 means 3 multiplied ________ times.

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Section B – Simplify the Following

1. $2^3 \times 2^2$23×22
2. $5^6 \div 5^2$56÷52
3. $(3^2)^3$(32)3
4. $7^0$70
5. $10^2 \times 10^3$102×103
6. $4^5 \div 4^3$45÷43
7. $(2^3)^2$(23)2
8. $9^1$91
9. $6^2$62
10. $8^2$82

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Section C – Multiple Choice Questions

1. Value of $2^4$24 is
   a) 8
   b) 12
   c) 16
   d) 24
2. $a^3 \times a^2$a3×a2 equals
   a) $a^5$a5
   b) $a^6$a6
   c) $a^1$a1
   d) $a^9$a9
3. Value of $10^0$100 is
   a) 0
   b) 1
   c) 10
   d) 100
4. Simplified form of $(x^2)^3$(x2)3 is
   a) $x^5$x5
   b) $x^6$x6
   c) $x^9$x9
   d) $x^8$x8
5. Value of $3^3$33 is
   a) 6
   b) 9
   c) 18
   d) 27

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Section D – Word Problems

1. A bacteria doubles every hour. If there are 2 bacteria initially, how many bacteria will there be after 5 hours?
2. Express 1,000,000 using exponents.
3. The side of a square is $5^2$52 cm. Find the area.
4. Write the standard form of 0.00045.
5. Simplify:
   $(2^2 \times 2^3) \div 2^4$(22×23)÷24

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Answer Key

Section A

1. 25
2. 1000
3. 32
4. 1
5. 4

Section B

1. $2^5 = 32$25=32
2. $5^4 = 625$54=625
3. $3^6 = 729$36=729
4. 1
5. $10^5 = 100000$105=100000
6. $4^2 = 16$42=16
7. $2^6 = 64$26=64
8. 9
9. 36
10. 64

Section C

1. c
2. a
3. b
4. b
5. d