Question

Scrieti sub forma de puteri urmatoarele numere naturale:

a)16;27;32;36;49;64;81;100;1024;2048;4096;2187;6541

b)5;25;125;652;3125;15625.

Answer 1

Răspuns:

Explicație pas cu pas:

16 = 4×4 = 4²

27 = 3 × 9 = 3³

32 = 16 x 2 = 2⁴x2 = 2⁵

36 = 6 x 6 = 6²

49 = 7²

64 = 8²

81 = 9²

100 = 10²

1024 = 16 x 64 = 4² x 4³ = 4⁽²⁺³⁾ = 4⁵

2048 = 1024 x 2 = (2²)⁵ x 2 = 2⁽¹⁰⁺¹⁾ = 2¹¹

4096 = 2048 x 2 = 2¹¹ x 2 = 2⁽¹¹⁺¹⁾ = 2¹²

2187 = 3 x 729 = 3 x 9 x 81 = 3 x 3² x 3⁴ = 3⁽¹⁺²⁺⁴) = 3⁷

71² = 5041 < 6541 < 6561 = 81²

__________________________________________

b)   5 = 5¹

25 = 5²

125 = 5 x 25 = 5 x 5² = 5⁽¹⁺²⁾ = 5³

625 = 5 x 125 = 5 x 5³ = 5⁽¹⁺⁴⁾ = 5⁴

3 125 = 5 x 625 = 5 x 5⁴ = 5⁽¹⁺⁴⁾ = 5⁵

15 625 = 5 x 3125 = 5 x 5⁵ = 5⁽¹⁺⁵⁾ = 5⁶