Question

[Đặng Hoàng Mỹ Anh]

so sánh các lũy thừa sau:

a.2³⁰⁰ và 3²⁰⁰

b.2⁹¹và 5³⁵

c.9¹²và 27⁷

Answer 1

[Anna]

a, \(2^{300}=2^{3.100}=8^{100}\)

\(3^{200}=3^{2.100}=9^{100}\)

Vì \(9^{100}>8^{100}\Rightarrow3^{200}>2^{300}\)

b, \(2^{91}=2^{13.7}=8192^7\)

\(5^{35}=5^{5.7}=3125^7\)

Vì \(8192^7>3125^7\Rightarrow2^{91}>5^{35}\)

c, \(9^{12}=\left(3^3\right)^{12}=3^{36}\)

\(27^7=\left(3^3\right)^7=3^{21}\)

Vì \(3^{36}>3^{21}\Rightarrow9^{12}>27^7\)

Answer 2

[Lưu Thiên Hương]

a) 2^300= 2^3.100=8^100

3^200=3^2.100=9^100

Vì 9^100>8^100 => 3^100>2^300

b) 2^91=2^13.7=8192^7

5^35=5^5.7=3195^7

Vì 8192^7>3125^7 => 2^91>5^35

c) 9^12=(3³)¹²=3^36

27^7=(3³)⁷=3^21

Vì 3^36>3^21 => 9^12>27^7