Question

ordonați crescător următoarele șiruri de numere naturale

Answer 1

a)   2⁵;  2⁷;  2⁰;  2⁹;   2⁴

2⁰;   2⁴;  2⁵;   2⁷;   2⁹ == > sir  crescator

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b) 5¹¹;  25⁶;   125⁵==>  5¹¹;   ( 5²) ⁶ = 5¹²;    ( 5³ ) ⁵ = 5¹⁵

5¹¹ <  5¹² <  5¹⁵ == >   5¹¹ <  25⁶  <   125⁵

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c)   8³⁰¹;  32¹¹⁹;    64⁸³  

8³⁰¹ = ( 2³ ) ³⁰¹ = 2⁹⁰³

32¹¹⁹ = ( 2⁵ ) ¹¹⁹ = 2 ⁵⁹⁵

64⁸³ = ( 2⁶ ) ⁸³ = 2⁴⁹⁸

2⁴⁹⁸  <  2⁵⁹⁵ <  2⁹⁰³ == >   64⁸³  <  32¹¹⁹  <  8³⁰¹

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d)   7²;   3²;    17²;   9²;   5²;   12²

3² <  5² < 7² <  9² <  12² <  17²  ==> sir crescator

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e) 100⁴;   1000³⁷;  10⁸⁰

100⁴ = ( 10² )⁴ = 10⁸

1000³⁷= ( 10³) ³⁷= 10¹¹¹

10 ⁸  < 10⁸⁰ <  10¹¹¹ ==>    100⁴  <   10⁸⁰  <  1000³⁷

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f)    36²¹;  6⁴³;   216¹⁵

36²¹ = ( 6² ) ²¹ = 6⁴²

216¹⁵ = ( 6³ ) ¹⁵ = 6⁴⁵

6⁴²  < 6⁴³ < 6⁴⁵  ==>   36²¹  <  6⁴³  <   216¹⁵

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g)     2⁴¹;   4²¹;   16¹¹

4²¹ = ( 2² ) ²¹ = 2⁴²

16¹¹ = ( 2⁴ ) ¹¹ = 2 ⁴⁴

2⁴¹  <   2 ⁴²  <  2 ⁴⁴ == >    2⁴¹ <  4²¹ <  16¹¹

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h)    25¹⁷;   5³³;   125¹²

25¹⁷ = ( 5² ) ¹⁷ = 5³⁴

125 ¹² = ( 5³ ) ¹² = 5³⁶

5³³ <  5³⁴ <  5³⁶ == >   5³³ <  25¹⁷  <  125¹²

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i )    243²⁷;   81³⁷;   27⁴⁷

243²⁷ = ( 3⁵ ) ²⁷ = 3¹³⁵

81 ³⁷ = ( 3⁴ )³⁷ = 3¹⁴⁸

27⁴⁷ = ( 3³ )⁴⁷ = 3¹⁴¹

3¹³⁵  <  3¹⁴¹  <   3¹⁴⁸ == >    243²⁷  <   27⁴⁷  <   81 ³⁷