Laws of Indices
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
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.