Kunci Jawaban Matematika Kelas 8 Halaman 24, Bab 1 Bilangan Perpangkatan

b. (3b)^-4

c. 6q^-5

d. a/4b^-5

e. 4c/16^-8

Jawaban:

a. 2^-2

= ½²

b. (3b)^-4

= 1/(3b)⁴

c. 6q^-5

= 6/q⁵

d. a/4b^-5

= ab^5/4

e. 4c/16^-8

= 2^2c/(2⁴)⁷
= 2^2c/2^-322
= 2³⁴

5. Sederhanakan bentuk berikut.

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
= 2^10-12
= 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

= 1,5^3+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

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

d. 8⁴ - 8²/2⁸

= (2³)⁴ - (2³)² / 2⁵
= 2¹²/2⁵ - 2⁶/2⁵
= 2^12-5 - 2^6-5
= 2^{7 - 2}

7. Sederhanakan bilangan berpangkat berikut dan tentukan nilai p.

a. 4²/2³ = 4p

b. (-4)²/2³ x 8⁴/(-16)² = 2^p

c. 9^p/4³ : 27²/2⁶ = 3⁸

d. (-9)²/5⁸ x 625²/(-81)⁴ = 3^p

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 = 2^p

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

c. 9^p/4³ : 27²/2⁶ = 3⁸

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

d. (-9)²/5⁸ x 625²/(-81)⁴ = 3^p

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

(Tribunnews.com/Yunita Rahmayanti)