Question

comparati numerele c.2⁸⁵ 16²²
d.125²⁶ 25³⁵
e.36¹¹² 6³³³
f.27⁸⁴ 9¹³⁰
g.2⁹¹ 64²⁴
h.121⁴⁵ 11⁹⁰
i.32⁹⁰ 16¹³⁵​

Answer 1

Răspuns:

Explicație pas cu pas:

c)   2⁸⁵ cu 16²²

16²² = ( 2⁴)²² = 2⁴ˣ²² = 2⁸⁸

=>  2⁸⁵ < 2⁸⁸ =>  2⁸⁵ < 16²²

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d)   125²⁶ cu   25³⁵

125²⁶ = ( 5³)²⁶ = 5³ˣ²⁶ = 5⁷⁸

25³⁵ = ( 5²)³⁵ = 5²ˣ³⁵ = 5⁷⁰

=>    5⁷⁸ >  5⁷⁰ =>    125²⁶  >   25³⁵

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e)    36¹¹²   si  6³³³

36¹¹² = (6²)¹¹² = 6²ˣ¹¹² = 6²²⁴

=>   6²²⁴  <   6³³³ =>    36¹¹²  <  6³³³

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f)   27⁸⁴  cu  9¹³⁰

27⁸⁴= ( 3³)⁸⁴ = 3³ˣ⁸⁴ = 3²⁵²

9¹³⁰ = ( 3²)¹³⁰ = 3²ˣ¹³⁰ = 3²⁶⁰

=>   3²⁵²  <  3²⁶⁰  =>    27⁸⁴  <   9¹³⁰

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g) 2⁹¹  cu   64²⁴

64²⁴ = ( 2⁶)²⁴ = 2⁶ˣ²⁴ = 2¹⁴⁴

=>   2⁹¹  <  2¹⁴⁴  =>   2⁹¹  <  64²⁴

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h)    121⁴⁵  cu  11⁹⁰

121⁴⁵ = ( 11²)⁴⁵ = 11²ˣ⁴⁵ = 11⁹⁰

=>    11⁹⁰ = 11⁹⁰    < =>  121⁴⁵ = 11⁹⁰

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i)    32⁹⁰  cu  16¹³⁵

32⁹⁰ = ( 2⁵)⁹⁰ = 2⁵ˣ⁹⁰ = 2⁴⁵⁰

16¹³⁵ = ( 2⁴)¹³⁵ = 2⁴ˣ¹³⁵ = 2⁵⁴⁰

=>    2⁴⁵⁰  <  2⁵⁴⁰   < = > 32⁹⁰  <   16¹³⁵