5.2.1 Indeks, Praktis Berformat PT3


5.2.1 Indeks, Praktis Berformat PT3
Soalan 1:
  (a) Permudahkan: a4 ÷ a7
  (b) Nilaikan: ( 2 4 ) 1 2 × 3 1 2 × 12 1 2  

Penyelesaian:
  (a) a4 ÷ a7 = a4-7 = a-3

(b)
( 2 4 ) 1 2 × 3 1 2 × 12 1 2 = 2 2 × 3 1 2 × ( 4×3 ) 1 2 = 2 2 × 3 1 2 × ( 2 2 ×3 ) 1 2 = 2 2 × 3 1 2 ×2× 3 1 2 = 2 3 ×3 =24


Soalan 2:
  (a) Permudahkan: p3 ÷ p-5
  (b) Nilaikan: 10 1 2 × 5 1 2 × ( 2 1 2 ) 5  

Penyelesaian:
  (a) p3 ÷ p-5 = p3-(-5) = p3+5 = p8

(b)
10 1 2 × 5 1 2 × ( 2 1 2 ) 5 = ( 2×5 ) 1 2 × 5 1 2 × 2 5 2 = 2 1 2 × 5 1 2 × 5 1 2 × 2 5 2 = 2 1 2 + 5 2 × 5 1 2 +( 1 2 ) = 2 3 + 5 1 2 1 2 = 2 3 + 5 0 =8+1 =9


Soalan 3:
  (a) Cari nilai bagi 10 4 3 ÷ 10 1 3 .  
  (b) Permudahkan (xy3)5 × x4.

Penyelesaian:
(a)
10 4 3 ÷ 10 1 3 = 10 4 3 1 3 = 10 3 3 =10
  
  (b)  ( x y 3 ) 5 × x 4 = x 5 y 15 × x 4    = x 5+4 y 15    = x 9 y 15


Soalan 4:
  (a) ( 81 a 8 ) 1 4 =    
  (b)  Cari nilai bagi  23 × 22

Penyelesaian:
(a)
( 81 a 8 ) 1 4 = 1 ( 81 a 8 ) 1 4  = 1 ( 3 4 ) 1 4 ( a 8 ) 1 4 = 1 3 a 2  

(b)
23 × 22 = 23+2 = 25 = 32


Soalan 5:
Cari nilai bagi setiap yang berikut.
  (a) 81 3 4 × 27 1    
  (b) 8 2 3 × 3 2  

Penyelesaian:
(a)
81 3 4 × 27 1 = ( 81 4 ) 3 × ( 3 3 ) 1 = ( 3 ) 3 × 3 3 = 3 3+( 3 ) = 3 0 =1

(b)
8 2 3 × 3 2 = ( 8 3 ) 2 × 1 3 2    = ( 2 ) 2 × 1 3 2    =4× 1 9    = 4 9


Soalan 6:
Cari nilai bagi setiap yang berikut.
  (a) 8 4 3 × ( 3 2 ) 3 × 9 3 2      
  (b) 2 2 × 3 2 2 3 ×81    

Penyelesaian:
(a)
8 4 3 × ( 3 2 ) 3 × 9 3 2 = ( 2 3 ) 4 3 × 3 6 × ( 3 2 ) 3 2 = 2 4 × 3 6 × 3 3 =16× 3 6+3 =16× 3 3 =16× 1 3 3 = 16 27  

(b)
2 2 × 3 2 2 3 ×81 = 2 2 × 3 2 2 3 × 3 4 = 2 2( 3 ) × 3 24 =2× 3 2 = 2 3 2 = 2 9

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