Bahas Bilangan Berpangkat Bulat, Soal Matematika Kelas 8 Halaman 24 Dibahas Tuntas!

a. (⅕)4/(⅕)5
b. (4/16)3/(8/32)2
c. 82/43 x 325/162
d. 32/43 : 8/27 x (⅔)3

Jawaban:

a. (⅕)4/(⅕)5

= (⅕)4-5
= (⅕)-1
= 1/(⅕)
= 1 x 5/1
= 5

b. (4/16)3/(8/32)2

= (24/24)3 / (23/25)2
= 26/212 / 26/210
= 26/212 x 210/26
= 210-12
= 2-2
= ½2

c. 82/43 x 325/162

= (23)2/(22)3 x (22)5/(24)2
= 26/26 x 225/28
= 217

d. 32/43 : 8/27 x (⅔)3

= 32/(22)3 x 27/8 x (2/4)3
= 32/26 x 33/23 x 23/33
= 32/26

6. Sederhanakan bilangan berpangkat berikut.

a. 1,53 x 1,54/1,55
b. (-4)3 : (-4)5/(-4)4
c. 92/94 - 44/47
d. 84 - 82/28

Jawaban:

a. 1,53 x 1,54/1,55

= 1,53+4-5
= 1,52

b. (-4)3 : (-4)5/(-4)4

= (-4)3/(-4)5 x (-4)4
= (-4)3/(-4)5+4
= (-4)3-9
= (-4)-6

c. 92/94 - 44/47

= 92-4 - 44-7
= 9-2 - 4-3
= 1/92 - 1/43

d. 84 - 82/28

= (23)4 - (23)2 / 25
= 212/25 - 26/25
= 212-5 - 26-5
= 27 - 2

7. Sederhanakan bilangan berpangkat berikut dan tentukan nilai p.

a. 42/23 = 4p
b. (-4)2/23 x 84/(-16)2 = 2p
c. 9p/43 : 272/26 = 38
d. (-9)2/58 x 6252/(-81)4 = 3p

Jawaban:

a. 42/23 = 4p

= 16/8 = 4p
= 2 = 4p
= 2/4 = p
= ½ = p
p = 1/2

b. (-4)2/23 x 84/(-16)2 = 2p

= 42 x 84 / 23 x 162 = 2p
= (22)2 x (23)4 / 23 x (24)2 = 2p
= 24 x 212 / 23 x 28 = 2p
= 24+12-3-8 = 2p
= 25 = 2p
p = 5

c. 9p/43 : 272/26 = 38

= 9p/43 x 26/272 = 38
= (32)p x 26 / (22)3 x (33)3 = 38
= 32p x 26 / 26 x 36 = 38
= 32p-6 = 38
= 2p - 6 = 8
= 2p = 8 + 6
= 2p/2 = 14/2
= p = 7

d. (-9)2/58 x 6252/(-81)4 = 3p

= 92 x 6252 / 58 x 814 = 3p
= (32)2 x (54)2 / 58 x (34)4 = 3p
= 34 x 58 / 58 x 316 = 3p
= 34-16 = 3p
= 312 = 3p
= p-12

(TribunNewsMaker.com/Muthiara 'Arsy/Tribunnews.com/Yunita Rahmayanti)