Question

compareaza puterile 16¹⁴si8²¹ si 25²⁵si 5⁴⁸​

Answer 1

Răspuns:

Explicație pas cu pas:

16^14 = (2^4)^14 = 2^56

8^21 = (2^3)^21 = 2^63

56 < 63

2^56 < 2^63

16^14 < 8^21

______________

25^25 = (5^2)^25 = 5^50

50 > 48

5^50 > 5^48

25^25 > 5^48

Answer 2

1.

${16}^{14} = { ({2}^{4}) } ^{14} = {2}^{4 \times 14} = {2}^{56}$

${8}^{21} ={( {2}^{3} )} ^{21} = {2}^{3 \times 21} = {2}^{63}$

Deci ${2}^{56} < {2}^{63} ( = ) {16}^{14} < {8}^{21}$

2.

${25}^{25} = {( {5}^{2} )} ^{25} = {5}^{50}$

Deci ${5}^{50} > {5}^{48} (= ) {25}^{25} > {5}^{48}$