Diberikan nilai p = 16, q = 9 dan r = 8 maka nilai paling sederhana dari( p^1/4 + q^1/2 . r^1/3 / p^1/2 . q^3/2 + r^2/3 )^-2

A.784
B. 196
C. 14
D. 1/14
E. 1/196

Kelas : 8
Mapel : Matematika
Kategori : Akar dan Pangkat
Kata Kunci : Sifat - sifat perpangkatan
Kode : 8.2.9 (Kelas 8 Matematika Bab 9 - Akar dan Pangkat)

Materi :

Sifat - sifat Perpangkatan :
1) (a^m) × (a^n) = a^(m + n)
2) (a^m) : (a^n) = a^(m - n)
3) (a^m)^n = a^(mn)
4) (ab)^n = (a^n) . (b^n)
=> (a/b)^n = (a^n)/(b^n)
5) a^0 = 1
6) a^-n = 1/(a^n)
=> (a/b)^-n = (b/a)^n

Pembahasan :

Diberikan nilai p = 16, q = 9 dan r = 8 maka nilai paling sederhana dari

[ p^(1/4) + q^(1/2) . r^(1/3) ]^(-2)
|-----------------------------------|
[ p^(1/2) . q^(3/2) + r^(2/3) ]

p = 16 = 2^4, maka :
p^(1/4) = 2^4(1/4) = 2^1 = 2
p^(1/2) = 2^4(1/2) = 2^2 = 4

q = 9 = 3^2, maka :
q^(1/2) = 3^2(1/2) = 3^1 = 3
q^(3/2) = 3^2(3/2) = 3^3 = 27

r = 8 = 2^3, maka :
r^(1/3) = 2^3(1/3) = 2^1 = 2
r^(2/3) = 2^3(2/3) = 2^2 = 4

Jadi nilai dari
[ p^(1/4) + q^(1/2) . r^(1/3) ]^(-2)
|-----------------------------------------|
[ p^(1/2) . q^(3/2) + r^(2/3) ]

= [ (2 + 3 . 2) / (4 . 27 + 4) ]^-2

= [ (2 + 6) / (108 + 4) ]^-2

= [(8)/(112)]^-2

= [1/14]^-2

= [14/1]^2

= 196

Keterangan :
^ = pangkat