Learn the Class 9 Madhyamik Mathematics Laws of Indices Formulas with clear explanations and solved examples. This chapter covers product rule, quotient rule, power rule, negative indices, zero index, rational indices, and equality of indices. A complete revision guide for school exams, homework, and Madhyamik preparation.
Chapter 02 – Laws of Indices | Class 9 Flash Formula
Product Rule : aᵐ × aⁿ = aᵐ⁺ⁿ
am × an = am + n
Example:
2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128
Quotient Rule : aᵐ ÷ aⁿ = aᵐ⁻ⁿ
am ÷ an = am-n
Example:
5⁶ ÷ 5² = 5⁶⁻² = 5⁴ = 625
Power of a Power Rule : (aᵐ)ⁿ = aᵐⁿ
(am)n = am×n
Example:
(3²)⁴ = 3²ˣ⁴ = 3⁸ = 6561
Product Raised to a Power : (ab)ᵐ = aᵐbᵐ
(ab)ᵐ = aᵐbᵐ
Example:
(2 × 5)³ = 2³ × 5³ = 8 × 125 = 1000
Quotient Raised to a Power : (a/b)ᵐ = aᵐ/bᵐ
({a\over b})^m = ({a^m\over b^m})
Example:
(4/3)² = 4²/3² = 16/9
Negative Index Rule : a⁻ⁿ = 1/aⁿ
a-n = 1\over \text{a}^n
Example:
2⁻³ = 1/2³ = 1/8
Rational Index Rule : ⁿ√a = a¹⁄ ⁿ
\sqrt[n]{a} = a^{1\over n}
Example:
³√8 = 8¹⁄ ³ = 2
Zero Index Rule : a⁰ = 1
a⁰ = 1
Example:
7⁰ = 1
Sign of Negative Base
(i) Even Power: (−a)m = am, if m is even
(ii) Odd Power (−a)m = −am, if m is odd
Example:
(−3)² = 9
(−3)³ = −27
Equality of Indices
When bases are same power are equal
If aᵐ = aⁿ, then m = n
Example:
2ˣ⁺¹ = 2⁵
x + 1 = 5
x = 4
You have reached the end.