Proszę o uzupełnienie przykładów. Dam naj .
Proszę o uzupełnienie przykładów. Dam naj .
Odpowiedź
1. a) (-2)⁵ = -32 (-2)⁻⁵ = (-1/2)⁵ = -1/32 2⁻⁵ = (1/2)⁵ = 1/32 b) (1/3)⁻² = 3² = 9 (-1/3)⁻² (-3)² = 9 (-1/3)⁻³ = (-3)³ = -27 c) (√3)⁴ = (3¹/²)⁴ = 3² = 9 (√3)⁻² = (3¹/²)⁻² = 3⁺¹ = 1/3 (√3)⁻⁶ = (3¹/²)⁻⁶ = 3⁻³ = (1/3)³ = 1/27 d) (√2)⁶ = (2¹/²)⁶ = 2³ = 8 (√2)⁷ = (2¹/²)⁷ = 2³·2¹/² = 8√2 (√2)⁻⁸ = (2¹/²)⁻⁸ = 2⁻⁴ = (1/2)⁴ = 1/16 2. a) 6⁻³·6⁵ = 6⁻¹⁺⁵ = 6² = 36 b) 4⁻⁸·4⁶ = 4⁻² = (1/4)² = 1/16 c) ((3/2)²)⁻² = (3/2)⁻⁴ = (2/3)⁴ = 16/81 d) (2/3)²·(2/3)⁻⁵ = (2/3)⁻³ = (3/2)³ = 27/8 e) 5⁷÷5¹⁰ = 5⁷⁻¹⁰ = 5⁻³ = (1/5)³ = 1/125 f) 7⁻⁴÷7⁻⁶ = 7⁻⁴⁺⁶ = 7² = 49 g) (3/4)⁻⁵÷(3/4)⁻³ = (3/4)⁻⁵⁺³ = (3/4)⁻² = (4/3)² = 16/9 h) (3/8)⁷÷(3/8)⁸ = (3/8)⁻¹ = 8/3 3. a) (2⁵)² = 2¹⁰ = 1024 b) (5⁻²)⁻² = 5⁴ = 625 c) ((3/2)²)⁻² = (3/2)⁻⁴ = (2/3)⁴ = 16/81 d) ((5/7)⁻¹)⁻²) = (5/7)² = 25/49 e) (3⁶)⁻²·3¹⁰ = 3⁻¹²·3¹⁰ = 3⁻² = (1/3)² = 1/9 f) ((6⁻²)⁵·6⁸ = 6⁻¹⁰·6⁸ = 6⁻² = (1/6)² = 1/36 g) (4⁻³)⁻⁴÷4⁹ = 4¹²÷4⁹ = 4³ = 64 4. a) 2³·4⁶ = 2³·(2²)⁶ = 2³·2¹² = 2¹⁵ b) 4⁻⁵·8² = (2²)⁻⁵·(2³)² = 2⁻¹⁰·2⁶ = 2⁻⁴ c) 64²÷32⁻³ = (2⁶)²÷(2⁵)⁻³ = 2¹²÷2⁻¹⁵ = 2²⁷ d) ((16⁻²÷4⁻⁸)·8⁴ = ((2⁴)⁻²÷(2²)⁻⁸)·(2³)⁴ = (2⁻⁸÷2⁻¹⁶)·2¹² = 2⁸·2¹² = 2²⁰ 5. a) x = 2⁴·4⁻² = 2⁴·(2²)⁻² = 2⁴·2⁻⁴ = 2⁴⁻⁴ = 2⁰ = 1 y = 4⁻⁴÷8⁻² = (2²)⁻⁴÷(2³)⁻² = 2⁻⁸÷2⁻⁶ = 2⁻² = (1/2)² = 1/4 x > y b) x = (2⁻⁴÷2⁻⁶)⁻¹ = (2²)⁻¹ = 2⁻² = (1/2)² = 1/4 y = (2⁻⁴·2⁻³)⁻¹ = (2⁻⁷)⁻¹ = 2⁷ = 128 y > x 6. a) (3√2)³ = 3³·(√2)³ = 27·(2¹/²)³ = 27·2³/² = 27·2√2 = 54√2 b) (2√3)⁴ = 2⁴·(√3)⁴ = 16·9 = 144 c) (2√2)⁵ = 2⁵·(√2)⁵ = 32·4√2 = 128√2 d) (2√5)⁶ = 2⁶·(√5)⁶ = 64·5³ = 64·125 = 8000 7. a) (-2√3)⁻² = (-2)⁻²·(√3)⁻² = (-1/2)²·(1/√3)² = 1/4 ·1/3 = 1/12 b) (3/√2)⁻⁴ = (√2/3)⁴ = 4/81 c) ((-√5/10)²)⁻¹ = (-√5/10)⁻² = (10/√5)² = 100/5 = 20 d) ((-3√2)⁻¹)⁻⁴ = (-3√2)⁴ = 81·4 = 324
1) a)(-2)⁵ = -32 (-2)⁻⁵ = (-1/2)⁵=-1/32 2⁻⁵ = (1/2)⁵=1/32 b)(1/3)⁻² = 3²=9 (-1/3)⁻² = (-3)²=9 (-1/3)⁻³ = (-3)³=-27 c)(√3)⁴ =(3¹/²)⁴ =3²= 9 (√3)⁻²=(3¹/²)⁻²=3⁻¹=1/3 (√3)⁻⁶ = (3¹/²)⁻⁶ = 3⁻³=(1/3)³=1/27 d)(√2)⁶ = (2¹/²)⁶ = 2³=8 (√2)⁷ = 8√2 (√2)⁻⁸ = (2¹/²)⁻⁸ = 2⁻⁴ = (1/2)⁴ = 1/16 2) a) 6⁻³ * 6⁵ = 6⁻³⁺⁵=6²=36 b)4⁻⁸ * 4⁶ = 4⁻²=1/16 c)(0,5)⁻⁴ * (0,5)⁻¹ = 0,5⁻⁵ = (5/10)⁻⁵ = (10/5)⁵ = 2⁵=32 d)(2/3)² * (2/3)⁻⁵ = (2/3)⁻³ = (3/2)³ = 27/8 e)5⁷ : 5¹⁰ = 5⁻³ = (1/5)³=1/125 f)7⁻⁴ : 7⁻⁶ = 7²=49 g)(3/4)⁻⁵ : (3/4)⁻³=(3/4)⁻² = (4/3)² =16/9 h)(3/8)⁷ : (3/8)⁸ = (3/8)⁻¹ = (8/3)¹=8/3 3) a)(2⁵)² = 2¹⁰=1024 b)(5⁻²)⁻² = 5⁴ = 625 c)((3/2)²)⁻² = (3/2)⁻⁴ = (2/3)⁴ = 16/81 d)((5/7)⁻¹)⁻² = (5/7)² = 25/49 e)(3⁶)⁻² *3¹⁰ = 3⁻¹²⁺¹⁰ = 3⁻²=(1/3)²=1/9 f)(6⁻²)⁵ * 6⁸ = 6⁻¹⁰⁺⁸ = 6⁻² = (1/6)²=1/36 g)(4⁻³)⁻⁴ : 4⁹ =4¹²⁻⁹ = 4³=64 h)(8⁴)⁻² : 8⁻¹⁰ = 8⁻⁸⁻ ⁻¹⁰ = 8⁻⁸⁺¹⁰=8²=64 4) a)2³ * 4⁶ = 2³ *(2²)⁶ = 2³* 2¹² = 2¹⁵ b)4⁻⁵ * 8² = (2²)⁻⁵ * (2³)² = 2⁻¹⁰ * 2⁶ = 2⁻⁴ c)64² : 32⁻³ = (2⁶)² : (2⁵)⁻³ = 2¹² : 2⁻¹⁵ = 2²⁷ d)(16⁻² : 4⁻⁸ )* 8⁴ = ((2⁴)⁻² : (2²)⁻⁸) *(2³)⁴ = (2⁻⁸ : 2⁻¹⁶)*2¹² = 2⁸ * 2¹²=2²⁰ 5)a) x = 2⁴ * 4⁻² = 2⁴ * (2²)⁻² = 2⁴ * 2⁻⁴ = 2⁰=1 y=4⁻⁴ : 8⁻² = (2²)⁻⁴ : (2³)⁻² = 2⁻⁸ : 2⁻⁶ = 2⁻² = (1/2)²=1/4 x>y b) x=(2⁻⁴:2⁻⁶)⁻¹ = (2²)⁻¹ = 2⁻² = (1/2)²=1/4 y=(2⁻⁴ * 2⁻³)⁻¹ = (2⁻⁷)¹ = 2⁷ = 128 x < y 6) a)(3√2)³ = 3√2*3√2*3√2 = 9*2 * 3√2 = 54√2 b)(2√3)⁴ = 2√3*2√3*2√3*2√3 = 4*3 *2√3*2√3 = 12* 12=144 c)(2√2)⁵ = 2√2*2√2*2√2*2√2*2√2 = 8 * 8 *2√2 = 128√2 d)(2√5)⁶ = 2√5 * 2√5 * 2√5 * 2√5 * 2√5 * 2√5 = 4*5 * 4*5 *4*5 = 20 *20*20 = =8000 7) a)(-2√3)⁻² = (-1/2√3)² = 1/12 b)(3/√2)⁻⁴ = (√2/3)⁴ = 4/81 c)((-√5/10)²)⁻¹ = (-√5/10)⁻² = (-10/√5)² = 100/5 = 20 d)((-3√2)⁻¹)⁻⁴ = (-3√2)⁴ =(-3√2) * (-3√2) *(-3√2)*(-3√2)=18*18= 324
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