tolongg kak dibantuuuuu... pleaseee
Answer (1)
Jawaban:1. Hitunglah nilai dari: - a) 5⁻³5⁻³ = 1 / 5³ = 1 / (5 * 5 * 5) = 1 / 125- b) 1 / 3²1 / 3² = 1 / (3 * 3) = 1 / 9 2. Sederhanakan: - a) A²⁰B⁵ / 3A³B¹⁰A²⁰B⁵ / 3A³B¹⁰ = (1/3) * A^(20-3) * B^(5-10) = (1/3) * A¹⁷ * B⁻⁵ = A¹⁷ / (3B⁵)- b) (3⁴2³5²)¹ / (3³ * 2⁴ * 5³)²(3⁴2³5²)¹ / (3³ * 2⁴ * 5³)² = (3⁴ * 2³ * 5²) / (3^(32) * 2^(42) * 5^(3*2)) = (3⁴ * 2³ * 5²) / (3⁶ * 2⁸ * 5⁶) = 3^(4-6) * 2^(3-8) * 5^(2-6) = 3⁻² * 2⁻⁵ * 5⁻⁴ = 1 / (3² * 2⁵ * 5⁴) = 1 / (9 * 32 * 625) = 1 / 180000- c) (216)¹/³ - (16)¹/⁴ + (125)²/³(216)¹/³ = ∛216 = 6(16)¹/⁴ = ⁴√16 = 2(125)²/³ = (∛125)² = (5)² = 25Jadi, 6 - 2 + 25 = 29 3. Hitunglah: - a) 3√12 + √27 - √1083√12 = 3√(4 * 3) = 3 * 2√3 = 6√3√27 = √(9 * 3) = 3√3√108 = √(36 * 3) = 6√3Jadi, 6√3 + 3√3 - 6√3 = 3√3- b) (3√6 - 2√5)²(3√6 - 2√5)² = (3√6)² - 2(3√6)(2√5) + (2√5)² = 9 * 6 - 12√(6*5) + 4 * 5 = 54 - 12√30 + 20 = 74 - 12√30- c) (2 + √3) / √5Untuk merasionalkan penyebut, kalikan dengan √5 / √5:(2 + √3) / √5 * (√5 / √5) = (2√5 + √15) / 5- d) (2√2 - 2√3) / (2√3 + 3√2)Untuk merasionalkan penyebut, kalikan dengan konjugatnya, yaitu (2√3 - 3√2) / (2√3 - 3√2):((2√2 - 2√3) / (2√3 + 3√2)) * ((2√3 - 3√2) / (2√3 - 3√2)) = (4√6 - 12 - 12 + 6√6) / (12 - 18) = (10√6 - 24) / -6 = (12 - 5√6) / 3 Ringkasan Jawaban: 1. a) 1/125b) 1/92. a) A¹⁷ / (3B⁵)b) 1 / 180000c) 293. a) 3√3b) 74 - 12√30c) (2√5 + √15) / 5d) (12 - 5√6) / 3
