Class 8 Mathematics – Exponents and Powers
These notes are prepared by Veezna Group of Institutes specially for Class 8 students. The chapter Exponents and Powers is explained step-by-step with many solved examples so that students can understand concepts clearly and score well in exams.
1. Meaning of Exponents
When the same number is multiplied repeatedly, we use exponents to write it in a short form.
Examples:
- 2 × 2 × 2 × 2 = 24
- 5 × 5 × 5 = 53
Here, the number being multiplied is called the base, and the number of times it is multiplied is called the exponent.
2. Laws of Exponents (With Solved Examples)
(a) Product of Powers
Rule: am × an = am+n
Solved Example 1:
23 × 24
= 2(3+4)
= 27
Solved Example 2:
52 × 53 = 55
(b) Quotient of Powers
Rule: am ÷ an = am−n (a ≠ 0)
Solved Example 1:
85 ÷ 82
= 8(5−2)
= 83
Solved Example 2:
106 ÷ 104 = 102
(c) Power of a Power
Rule: (am)n = am×n
Solved Example:
(32)4
= 3(2×4)
= 38
(d) Power of a Product
Rule: (ab)m = am × bm
Solved Example:
(2 × 5)3
= 23 × 53
= 8 × 125 = 1000
(e) Power of a Quotient
Rule: (a / b)m = am / bm
Solved Example:
(4 / 5)2
= 42 / 52
= 16 / 25
3. Zero Exponent
Rule: a0 = 1 (a ≠ 0)
Solved Examples:
- 70 = 1
- 1000 = 1
4. Negative Exponents
Rule: a−m = 1 / am
Solved Examples:
- 2−3 = 1 / 23 = 1 / 8
- 5−2 = 1 / 25
5. Standard Form (Scientific Notation)
Very large or very small numbers are written in standard form as:
a × 10n, where 1 ≤ a < 10
Solved Example 1:
500000 = 5 × 105
Solved Example 2:
0.00036 = 3.6 × 10−4
Important Exam-Oriented Questions
Very Short Answer
- Write 63 in expanded form.
- Find the value of 90.
Short Answer
- Simplify: 43 × 42
- Find the value of (23)2
Long Answer
- Explain laws of exponents with suitable examples.
- Express 7200000 in standard form.
Key Points for Exams
- Always apply correct law of exponents.
- Be careful with negative and zero powers.
- Write steps clearly to get full marks.
Prepared with care by Veezna Group of Institutes for learning support and exam preparation.
