Question

Порівняйте між собою числові вирази 1) 49⁸і 7¹⁶ 2) 2⁴⁰ і 3⁸⁰

Answer 1

Ответ:

1) 49⁸ = 7¹⁶

2) 2⁴⁰< 3⁸⁰

Объяснение:

1) 49 у 8 степені і 7 у 16 степені

49⁸ V 7¹⁶

(7²)⁸ V 7¹⁶

7¹⁶ = 7¹⁶⇒ 49 у 8 степені = 7 у 16 степені

2) 2 у 40 степені і 3 у 80 степені

2⁴⁰< 3⁸⁰

Answer 2

1) 49⁸ and 7¹⁶: To compare these two expressions, we can calculate their values.

49⁸ = 49 * 49 * 49 * 49 * 49 * 49 * 49 * 49 = 2,417,851,639,229,258,349

7¹⁶ = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 18,446,744,073,709,551,616

Comparing the two values, we can see that 7¹⁶ is significantly larger than 49⁸.

2) 2⁴⁰ and 3⁸⁰: Again, we can calculate the values of these expressions to compare them.

2⁴⁰ = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1,099,511,627,776

3⁸⁰ = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 405,648,192,073,033,408,478,945,025,720,32

Comparing the two values, we can see that 3⁸⁰ is significantly larger than 2⁴⁰.