SIFAT-SIFAT BILANGAN BERPANGKAT
Sifat-sifat bilangan berpangkat dan contohnya, serta Soal Latihan dan jawaban!
Sifat-sifat bilangan berpangkat yang saya ketahui ada 7 macam, diantaranya :
1. a^m × aⁿ = a^m+ⁿ
2. a^m / aⁿ = a^m-ⁿ
3. (a^m)ⁿ= a^m×ⁿ
4. (a×b)ⁿ = aⁿ× bⁿ
5. (a/b)ⁿ= aⁿ/bⁿ
6. a° = 1
7. a-ⁿ= 1/aⁿ
*(^) = pangkat
Contohnya :
= 2⁵ = 32
= 4² = 16
= 2⁶= 64
= 4³ × 10³ = 64 × 1000
= 64000
= 9/16
= 4° = 1
= 4-²
= 1/4² = 1/16
= 2a⁸ / 8a¹⁰
= 1/4a⁸-¹⁰
= 1/4 a-²
= 1/4a²
= 4a⁶-¹b³-⁸
= 4a⁵b-⁵
= 4a⁵/b⁵
Soal Latihan :
1. (1/4)³ =
2. (2/5)³ =
3. 3⁵ × 3⁻³ =
4. 6⁸ × 6⁵ =
5. (3²)² =
6. 10³/10⁸ =
7. 9²/9² =
8. (4a²)³ =
9. 6a³ × 2a⁷ / 4a⁶ =
10. 8a⁻³ × b⁴ / 12a² × 3b⁻¹ =
Jawaban :
1. (1/4)³ = 1/4 × 1/4 ×1/4
= 1/16
2. (2/5)³ = 2/5 ×2/5× 2/5
= 8/125
3. 3⁵ × 3⁻³ = 3⁵⁺⁽⁻³⁾
= 3²
= 9
4. 6⁸ × 6⁵ = 6⁸⁻⁵
= 6³
= 216
5. (3²)² = 3²ˣ²
= 3⁴
= 81
6. 10³/10⁸ = 10³⁻⁸
= 10⁻⁵
= 1/10⁵
= 1/100000
7. 9²/9² = 9²⁻²
= 9⁰
= 1
8. (4a²)³ = 4³a²ˣ³
= 64a⁶
9. 6a³ × 2a⁷ / 4a⁶ = 12a³⁺⁷/4a⁶
= 12a¹⁰/4a⁶
= 3a¹⁰⁻⁶
= 3a⁴
10. 8a⁻³ × b⁴ / 12a² × 3b⁻¹ = 8a⁻³b⁴ / 36a²b
= 2/9 a⁻³⁻²b⁴⁻⁽⁻¹⁾
= 2/9 a⁻⁵b⁵
= 2b⁵/9a⁵
Soal Latihan :
1. (1/4)³ =
2. (2/5)³ =
3. 3⁵ × 3⁻³ =
4. 6⁸ × 6⁵ =
5. (3²)² =
6. 10³/10⁸ =
7. 9²/9² =
8. (4a²)³ =
9. 6a³ × 2a⁷ / 4a⁶ =
10. 8a⁻³ × b⁴ / 12a² × 3b⁻¹ =
Jawaban :
1. (1/4)³ = 1/4 × 1/4 ×1/4
= 1/16
2. (2/5)³ = 2/5 ×2/5× 2/5
= 8/125
3. 3⁵ × 3⁻³ = 3⁵⁺⁽⁻³⁾
= 3²
= 9
4. 6⁸ × 6⁵ = 6⁸⁻⁵
= 6³
= 216
5. (3²)² = 3²ˣ²
= 3⁴
= 81
6. 10³/10⁸ = 10³⁻⁸
= 10⁻⁵
= 1/10⁵
= 1/100000
7. 9²/9² = 9²⁻²
= 9⁰
= 1
8. (4a²)³ = 4³a²ˣ³
= 64a⁶
9. 6a³ × 2a⁷ / 4a⁶ = 12a³⁺⁷/4a⁶
= 12a¹⁰/4a⁶
= 3a¹⁰⁻⁶
= 3a⁴
10. 8a⁻³ × b⁴ / 12a² × 3b⁻¹ = 8a⁻³b⁴ / 36a²b
= 2/9 a⁻³⁻²b⁴⁻⁽⁻¹⁾
= 2/9 a⁻⁵b⁵
= 2b⁵/9a⁵
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