eksponen jangan ngaco anjir ​

Jawaban:Oke, mari kita sederhanakan soal-soal ini: 1. Hitunglah: - a. (2⁻³ × 9⁻²) / 18⁻³ + (6¹² × 24⁻²) / 12³ = 2⁻³ × 3⁻⁴ × (2⁻³ × 3²)⁻¹ + (2¹² × 3¹² × 2⁻⁶ × 3⁻²) / (2⁶ × 3³) = 2⁻³ × 3⁻⁴ × 2³ × 3⁻⁶ + (2⁶ × 3¹⁰) / (2⁶ × 3³) = 3⁻¹⁰ + 3⁷ = 3⁻¹⁰(1 + 3¹⁷)- b. (7² × 2⁻³ × 5³ - 5² × 7 × 2²) / (7² × 2⁻¹ × 5²) = (49 × 1/8 × 125 - 25 × 7 × 4) / (49 × 1/2 × 25) = (765.625 - 700) / 612.5 = 65.625 / 612.5 = 0.107 2. Sederhanakan: - a. (70x⁻³y⁻⁴z²) / (25x²y⁻⁷z⁻³) = (14/5) x⁻⁵ y³ z⁵- b. ((x⁻⁶y⁻²) / (y⁻⁵z³))¹¹ = (x⁻⁶y³z⁻³)¹¹ = x⁻⁶⁶ y³³ z⁻³³- c. ((x⁻²y⁵z⁻³) / (x⁴y⁻²z⁻²))⁻³ = (x⁻⁶y⁷z⁻¹)⁻³ = x¹⁸ y⁻²¹ z³ 3. Bentuk Pangkat Positif: - a. (ab⁻¹ - a⁻¹b) / (a⁻¹ + b⁻¹) = (a/b - b/a) / (1/a + 1/b) = ((a² - b²) / ab) / ((a + b) / ab) = (a² - b²) / (a + b) = (a - b)(a + b) / (a + b) = a - b- b. ((a⁻¹ - b⁻¹) / (a⁻² - b⁻²))⁻¹ = ((1/a - 1/b) / (1/a² - 1/b²))⁻¹ = (((b - a) / ab) / ((b² - a²) / a²b²))⁻¹ = (((b - a) / ab) / ((b - a)(b + a) / a²b²))⁻¹ = (ab / (b + a)) 4. Sederhanakan: - a. ((2⁴xy⁻⁵) / (3⁵y²))⁻¹ ((2²x⁻²y⁻¹) / (3x⁻³y))² = ((3⁵y²) / (2⁴xy⁻⁵)) ((2⁴x⁻⁴y⁻²) / (3²x⁻⁶y²)) = (3⁵y⁷ / 2⁴x) (2⁴x⁻⁴y⁻² / 3²x⁻⁶y²) = 3³x²y³- b. ((a + b)⁻¹ (a⁻² - b⁻²)) / ((a⁻¹ + b⁻¹) (ab⁻¹ - a⁻¹b)) = ((1 / (a + b)) ((1/a²) - (1/b²))) / (((1/a) + (1/b)) ((a/b) - (b/a))) = (((b² - a²) / a²b²) / (a + b)) / (((a + b) / ab) ((a² - b²) / ab)) = ((b - a)(b + a) / (a²b²)(a + b)) / (((a + b)(a - b)(a + b)) / (a²b²)) = (b - a) / ((a + b)(a - b)) = -1 / (a + b) 5. Sederhanakan: - a. 2^(n+1) × 4^(n-1) × 8^(n+2) × 16^(n-2) = 2^(n+1) × 2^(2n-2) × 2^(3n+6) × 2^(4n-8) = 2^(n+1+2n-2+3n+6+4n-8) = 2^(10n - 3)- b. (27^(n+2) × 24^(2n-3)) / 36^(2(n-4)) = (3^(3n+6) × (2³ × 3)^(2n-3)) / (2² × 3²)^(2n-8) = (3^(3n+6) × 2^(6n-9) × 3^(2n-3)) / (2^(4n-16) × 3^(4n-16)) = (3^(5n+3) × 2^(6n-9)) / (2^(4n-16) × 3^(4n-16)) = 3^(n+19) × 2^(2n+7) Soal 5b: (27^(n+2) × 24^(2n-3)) / 36^(2(n-4)) Langkah-langkah: 1. Ubah Basis ke Bilangan Prima:- 27 = 3³- 24 = 2³ × 3- 36 = 2² × 3²- Sehingga: (3^(3(n+2)) × (2³ × 3)^(2n-3)) / (2² × 3²)^(2(n-4))2. Distribusi Pangkat:- (3^(3n+6) × 2^(6n-9) × 3^(2n-3)) / (2^(4n-8) × 3^(4n-8))3. Gabungkan Suku Sejenis (Basis Sama):- (3^(3n+6 + 2n-3) × 2^(6n-9)) / (2^(4n-8) × 3^(4n-8))- (3^(5n+3) × 2^(6n-9)) / (2^(4n-8) × 3^(4n-8))4. Sederhanakan dengan Mengurangkan Pangkat (Jika Basis Sama):- 3^(5n+3 - (4n-8)) × 2^(6n-9 - (4n-8))- 3^(5n+3 - 4n + 8) × 2^(6n-9 - 4n + 8)- 3^(n+11) × 2^(2n-1) Jawaban Akhir: Bentuk sederhana dari (27^(n+2) × 24^(2n-3)) / 36^(2(n-4)) adalah 3^(n+11) × 2^(2n-1). Semoga ini membantu!

Answered by ara1412 | 2025-08-09