Question

Proszę o zrobienie i wytłumaczenie mi tych 6 zadań na ABC z dwóch grup.

Z góry dziękuję ;D

Answer 1

Grupa A

1. C. -3,1⁰  

   -3,1⁰ = -1

2.  B. 289,  bo 17² = 289

3.  A. 2⁷

    24⁷÷12⁷ = (24/12)⁷ = 2⁷

4.  D. 7¹⁷

    7¹²·7⁵ = 7¹²⁺⁵ = 7¹⁷

5.  B. 7 ²⁴

    (7⁶)⁴ = 7⁶·⁴ = 7²⁴

6.  B. 36x⁴y²

     (6x²y)² = 36x⁴y²

7.

a)   9⁷÷3 = (3²)⁷÷3 = 3¹⁴÷3 = 3¹⁴⁻¹ = 3¹³

b)   2¹⁰ = 1024,  to 2⁹ = 1024/2 = 512

8.

a)   (-3/4)⁵ < -3/4

b)   0,1³ > 0,1⁴

c)   2⁵·5¹²/5¹¹·2² < 2³·5²

      2⁵·5¹²/5¹¹·2² = 2⁵⁻²·5¹²⁻¹¹ = 2³·5 < 2³·5²

9.

P = a·h/2 = 2⁸·32/2 = 2⁸·2⁵/2 = 2¹³⁻¹ = 2¹² 

10.

a)   521 km = 521 000 000 m = 5,21·10⁸ m

b)   0,71 cm = 0,0071 m = 7,1·10⁻³ m

11.

a1 = 6·10⁻³ m

P1 = a1² = (6·10⁻³m)² = 36·10⁻⁶ m²

a2 = 4·10⁻⁵ m

P2 = a2² = (4·10⁻⁵m)² = 16·10⁻¹⁰ m²

P1/P2 = 36·10⁻⁶/16·10⁻¹⁰ = 2,25·10⁴

12.

a)   5⁻¹²·(5⁻³÷5)⁻¹/(5⁻²)⁴ = 5⁻¹²·(5⁻⁴)⁻¹/5⁻⁸ = 5⁻¹²·5⁴/5⁻⁸ = 5⁻⁸/5⁻⁸ = 1

b)   2⁷·5⁷/10⁷ · 1,3⁴·81/3,9³ = 10⁷/10⁷ · 1,3⁴·3⁴/3,9³ = 1·(1,3·3)⁴/3,9³ = 3,9⁴/3,9³ = 3,9

c)   25²·5²/125 = (5²)²·5²/5³ = 5⁴·5²/5³ = 5⁶/5³ = 5³ = 125

*13.

31¹³ ... 17¹⁷

 

31¹³ < 32¹³ = (2⁵)¹³ = 2⁶⁵

31¹³ < 2⁶⁵

 

17¹⁷ > 16¹⁷ = (2⁴)¹⁷ = 2⁶⁸

17¹⁷ > 2⁶⁸

 

31¹³ < 2⁶⁵ < 2⁶⁸ < 17¹⁷

31¹³ < 17¹⁷

 

Grupa B

1. B. 324 , bo 18² = 324

2. A. -6,2² 

        -(6,2)² = -6,2²

3. C.8¹⁵

    (8³)⁵ = 8³·⁵ = 8¹⁵

4. C. 2⁹

    34⁹÷17⁹ = (34/17)⁹ = 2⁹

5. D. 6¹⁷

    6¹⁴·6³ = 6¹⁴⁺³ = 6¹⁷

6. B. 16x⁴y²

   (4x²y)² = 16x⁴y²

7.

a)   (-3/7)⁵ < -3/7

b)   0,2² > 0,2³

c)   2³·3⁴ > 2⁵·3¹⁵/3¹¹·2³ = 2⁵⁻³·3¹⁵⁻¹¹ = 2²·3⁴

d)   (1/9)⁻² = 9² = (3²)² = 3⁴ < 3⁵

8.

a)   16³÷4 = (4²)³÷4 = 4⁶÷4 = 4⁶⁻¹ = 4⁵

b)   4⁵ = 1024, to 4⁶ = 1024*2 = 2048

9.

P = a·h/2 

P = 2¹⁰·16/2 = 2¹⁰·2⁴/2 = 2¹⁴⁻¹ = 2¹³

10.

a1 = 6·10⁻⁵ m

P1 = a1² = (6·10⁻⁵m)² = 36·10⁻¹⁰ m²

a2 = 4·10⁻⁷ m

P2 = a2² = (4·10⁻⁷m)² = 16·10⁻¹⁴ m²

P1/P2 = 36·10⁻¹⁰/16·10⁻¹⁴ = 2,25·10⁻¹⁰⁺¹⁴ = 2,25·10⁴

11.

a)   730 m = 730 000 mm = 7,3·10⁵ mm

b)   0,43 cm = 0,0043 m = 4,3·10⁻³ m

12.

a)   7⁻¹¹·(7⁻⁴÷7)⁻¹/(7⁻³)² = 7⁻¹¹·(7⁻⁵)⁻¹/7⁻⁶ = 7⁻¹¹·7⁵/7⁻⁶ = 7⁻¹¹⁺⁵/7⁻⁶ = 7⁻⁶/7⁻⁶ = 1

b)  1,3⁴·16/2,6³ · 10⁹/5⁹·2⁹ = 1,3⁴·2⁴/(1,3·2)³ ·(5·2)⁹/5⁹·2⁹ = 1,3⁴·2⁴/1,3³·2³ ·5⁹·2⁹/5⁹·2⁹ = 1,3·2·1 = 2,6

c)   4³·16³/64² = 4³·(4²)³/(4³)² = 4³·4⁶/4⁶ = 4³ = 64

*13.

31¹⁵ ... 17¹⁹

 

31⁵ < 32¹⁵ = (2⁵)¹⁵ = 2⁷⁵

31¹⁵ < 2⁷⁵

 

17¹⁹ > 16¹⁹ = (2⁴)¹⁹ = 2⁷⁶

17¹⁹ > 2⁷⁶

2⁷⁵ < 2⁷⁶

 

31¹⁵ < 2⁷⁵ < 2⁷⁶ < 17¹⁹

31¹⁵ < 17¹⁹