INDICES

RULES OF INDICES -BRACKET

RULE OF INDICES (PETUA INDEKS)

SAME BASE (ASAS SAMA)

(aⁿ)^m = a^{n × m}

Example : Simplify the following

(Permudahkan yang berikut)

(a)        (m⁵)⁷       

Solution: (m⁵)⁷ = m^5×7 = m³⁵

(b)        (3⁴)⁶  

Solution:   (3⁴)⁶ = 3^4×6 = 3²⁴

RULES OF INDICES - DIVISION

RULE OF INDICES (PETUA INDEKS)

SAME BASE (ASAS SAMA)

aⁿ ÷ a^m = a^{n – m}

Example : Simplify the following

(Permudahkan yang berikut)

(a)        m⁵ ÷ m³          

Solution:

m⁵ ÷ m³   

= m^{5 – 3}  

= m²

(b)        4r⁷ ÷ 2r           

Solution:

4r⁷ ÷ 2r 

= (4 ÷ 2)r^{7 – 1}  

= 2r⁶

(c)         – 4w⁵ ÷ (– 4 w⁴)   

Solution: 

– 4w⁵ ÷ (– 4 w⁴)

   = (– 4) ÷ (– 4) w^{5 – 4}

   = w

RULES OF INDICES (MULTIPLY)

RULE OF INDICES (PETUA INDEKS)

SAME BASE (ASAS SAMA)

aⁿ × a^m = a^{n + m}

Example : Simplify the following

(Permudahkan yang berikut)

(a)        m³ × m⁴          

 

Solution: 

m³ × m⁴  

= m³⁺⁴ 

= m⁷

(b)        3p³ × 2p  

Solution: 

3p³ × 2p 

= (3 × 2) p³⁺¹  

= 6p⁴

(c)         4r³ × 5p² × r²

Solution: 

4r³ × 5p × r² 

= (4×5) r³⁺²p

= 20r⁵p