Rules of Indices

aᵐ x aⁿ = a ᵐ⁺ⁿ

Examples

1. t⁴ x t⁵ = t⁹

2. m⁴ x m⁻⁵ = m⁻¹

3. a⁴ x a³ x a⁻² x a⁵ = a¹⁰

REMINDER: 1 can be missing.

aᵐ / aⁿ = aᵐ⁻ⁿ

Examples

1. x¹¹ / x⁷ = x⁴

2. t⁻⁷ / t⁻⁴ = t⁻³

(aᵐ)ⁿ = aᵐˣⁿ

Examples

1. (3x²)³

= 3³ (x²)³

= 27x⁶

2. (-2x²)⁵

= (-2)⁵ (x²)⁵

= 32x¹⁰

a⁰ = 1

aᵐ ⁼ 1/a⁻ᵐ

1. (t⁻²)³

= t⁻⁶

= 1/t⁶

2. (t⁴/t¹⁰)³

= (t⁻⁶)³

= t⁻¹⁸

= 1/t¹⁸

aᵐ/ⁿ = ⁿ√aᵐ

1. 2ˣ²/³ 

= 2 x ³√ˣ²

2. 5t⁻⁴/⁵ 

= 5 x 1/t⁴/⁵ 

= 5/5√t⁴

16¹/²

= ²√16¹

= √16

= 4

8³/⁵

= ³√8⁵

= 2⁵

= 32