Question

Coronița!Comparați numerele dar arătați cum ati calculat va rog.. acest semn ^ inseamna ,,la puterea"
1)
a.8^18 - 7 × 8^17 cu 16^14 - 15 × 16^13

d. 49^28 - 7^55 cu 7^57 - 6 × 7^56

e. (8^13 × 4^15)^3 cu (16^9 × 32^7)^2 × 64^11

b.27^13 - 26 × 27^12 cu 9^19 - 8 × 9^18

c. 5^38 - 24 × 25^18 cu 125^13 - 124 × 125^12

f. (9^15 × 3^14)^4 cu (81^3 × 27^7)^3 × 243^15

Answer 1

1)
a.8¹⁸ - 7 × 8¹⁷=8¹⁷(8-7)=8¹⁷=(2³)¹⁷=2⁵¹

  16¹⁴ - 15 × 16¹³=16¹³(16-15)=16¹³=(2⁴)¹³=2⁵²
2⁵¹<2⁵²

d. 49²⁸ - 7⁵⁵ =(7²)²⁸-7⁵⁵=7⁵⁶-7⁵⁵=7⁵⁵(7-1)=7⁵⁵x6

 7⁵⁷ - 6 × 7⁵⁶=7⁵⁶(7-6)=7⁵⁶
7⁵⁵x6<7⁵⁶

e. (8¹³× 4¹⁵)³ =[(2³)¹³x(2²)¹⁵]³=(2³⁹x2³⁰)³=(2³⁹⁺³⁰)³=(2⁶⁹)³= 2²°⁷

(16⁹ × 32⁷⁷)² × 64¹¹=[(2⁴)⁹x(2⁵)⁷]²x(2⁶)¹¹=(2³⁶x2³⁵)²x2⁶⁶=
(2³⁶⁺³⁵)²x2⁶⁶=(2⁷¹)²x2⁶⁶=2¹⁴²x2⁶⁶=2¹⁴²⁺⁶⁶=2²²°⁸
2²°⁷<2²²°⁸

b.27¹³ - 26 × 27¹² =27¹²(27-26)=27¹²=(3³)¹²=3³⁶

 9¹⁹- 8 × 9¹⁸=9¹⁸(9-8)=9¹⁸=(3²)¹⁸=3³⁶
puterile sunt egale

c. 5³⁸- 24 × 25¹⁸=5³⁸-24x(5²)¹⁸ =5³⁸-24x5³⁶=5³⁶(5²-24)=5³⁶(25-24)=5³⁶

 125¹³ - 124 × 125¹²=125¹²(125-124)=125¹²=(5³)¹²=5³⁶
puterile sunt egale

f. (9¹⁵× 3¹⁴)⁴=[(3²)¹⁵x3¹⁴)⁴=(3³°x3¹⁴)⁴=(3³°⁺¹⁴)⁴=(3⁴⁴)⁴=3¹⁷⁶

  (81³ × 27⁷)³ × 243¹⁵=[(3⁴)³x(3³)⁷]³x(3⁵)¹⁵=(3¹²x3²¹)³x3⁷⁵=(3¹²⁺²¹)³x3⁷⁵=
(3³³)³x3⁷⁵=3⁹⁹x3⁷⁵=3⁹⁹⁺⁷⁵=3¹⁷⁴
3¹⁷⁶>3¹⁷⁴