Comparati puterile:a)8la puterea a 8 si4la puterea a 12
b)8la puterea 57 si 9 la puterea 57
c)2 la puterea 15 si 3 la puterea 10
d)3 la puterea 30 si 5 la puterea 20
e)16 la puterea a 15 si 2 la puterea 60

Răspuns

Explicație pas cu pas:

a) 8⁸ = ( 2³)⁸ = 2²⁴

4¹² = ( 2²)¹² = 2²⁴

=>    2²⁴ = 2²⁴ ==>   8⁸ = 4¹²

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b)     8⁵⁷ < 9⁵⁷   ( 8 < 9 ) bazele;   57 = 57 ( exponentii )

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c)  

2¹⁵ = ( 2³ )⁵ = 8⁵

3¹⁰ = ( 3²)⁵ = 9⁵

=>  8⁵ < 9⁵ ;   ( 8 < 9 ) ==>   2¹⁵ < 3¹⁰

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d)

3³⁰ = ( 3³ )¹⁰ = 27¹⁰

5²⁰ = ( 5²)¹⁰ = 25¹⁰

=>   27¹⁰ > 25¹⁰  ==>   3³⁰ >  5²⁰

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e)

16¹⁵ = ( 2⁴)¹⁵ = 2⁶⁰

==>   2⁶⁰ = 2⁶⁰ ==>   16¹⁵ = 2⁶⁰