Răspuns:
a) 2¹¹ · 5¹⁰ < 10¹¹
b) 15¹⁵ < 3¹⁴·5¹⁵
c) 14¹⁶ < 2¹⁷·7¹⁶
d) 21²⁵> 3²⁴·7²⁵
e) 4¹¹·5²² = 10²²
f) 9¹²·5²³ > 15²³
g) 8⁹·5²⁸ > 10²⁷
h) 7³⁵·8¹² > 14³⁵
Explicație pas cu pas:
a) 2¹¹ · 5¹⁰ = 2·2¹⁰·5¹⁰ = 2·(2·5)¹⁰ = 2·10¹⁰
10¹¹ = 10·10¹⁰
Cum 2<10 ⇒ 2·10¹⁰ < 10·10¹⁰
b) 15¹⁵ = (3·5)¹⁵ = 3¹⁵·5¹⁵ < 3¹⁴·5¹⁵
c) 14¹⁶ = (2·7)¹⁶ = 2¹⁶·7¹⁶ < 2¹⁷·7¹⁶
d) 21²⁵ = (3·7)²⁵ = 3²⁵·7²⁵ > 3²⁴·7²⁵
e) 4¹¹·5²² = (2²)¹¹·5²² = 2²²·5²² = (2·5)²² = 10²²
f) 9¹²·5²³ = (3²)¹²·5²³= 3²⁴·5²³ = 3·(3·5)²³ = 3·15²³>15²³
g) 8⁹·5²⁸ = (2³)⁹·5²⁸ = 2²⁷·5²⁸ = (2·5)²⁷·5 = 10²⁷·5 > 10²⁷
h) 7³⁵·8¹² = 7³⁵·(2³)¹² = 7³⁵·2³⁶ = (7·2)³⁵·2 = 14³⁵·2 > 14³⁵
