4.1.2 Indeks dan Hukum Indeks (Bahagian 2)
(C) Indeks PecahanSecara amnya, bagi semua a a 1 n = a n a m n = a m n = ( a n ) m ∗ a n disebut punya kuasa n bagi a. ∗ ( a n ) m disebut kuasa m bagi punya kuasa n bagi a.
Contoh 1:
Cari nilai-nilai yang berikut:
(a) 81
1
2
(b) 64
1
3
(c) 625
1
4
Penyelesaian:
(a) 81
1
2
=
81
=
9
(b) 64
1
3
=
64
3
=
4
(c) 625
1
4
=
625
4
=
5
Contoh 2:
Cari nilai-nilai yang berikut:
(a)
16
3
2
(b)
(
27
64
)
2
3
Penyelesaian:
(a)
16
3
2
=
(
16
1
2
)
3
=
4
3
=
64
(b)
(
27
64
)
2
3
=
(
27
64
3
)
2
=
(
3
4
)
2
=
9
16
(D) Hukum-hukum Indeks
a m × a n = a m+n Contoh: 3 3 × 3 2 = 3 3+2 = 3 5 =243
a m ÷ a n = a m−n atau a m a n = a m−n ,a≠0 Contoh: 3 3 ÷ 3 2 = 3 3−2 = 3 1 =3 atau 3 3 3 2 = 3 3−2 = 3 1 =3
( a m ) n = a mn Contoh: ( 7 3 ) 4 = 7 3×4 = 7 12
( a b ) n = a n b n Contoh: ( 15 ) 3 = ( 5 × 3 ) 3 = 2 3 × 3 3
( a b ) n = a n b n , b≠0 Contoh: ( 3 5 ) 4 = 3 4 5 4 = 81 625