Question

[trần đức thuận]

1) (2²⁰¹⁶+2²⁰¹⁷+2²⁰¹⁸):(2²⁰¹⁴+2²⁰¹⁵+2²⁰¹⁶) =?

2) so sánh:

3⁵⁰⁰và 7³⁰⁰

Answer 1

[Nguyễn Nam]

a) \(\left(2^{2016}+2^{2017}+2^{2018}\right):\left(2^{2014}+2^{2015}+2^{2016}\right)\)

\(=\dfrac{2^{2016}+2^{2017}+2^{2018}}{2^{2014}+2^{2015}+2^{2016}}\)

\(=\dfrac{2^{2016}\left(1+2+2^2\right)}{2^{2014}\left(1+2+2^2\right)}\)

\(=\dfrac{2^{2016}}{2^{2014}}\)

\(=2^{2016-2014}\)

\(=2^2\)

\(=4\)

b)

\(3^{500}=3^{5.100}=\left(3^5\right)^{100}=243^{100}\)

\(7^{300}=7^{3.100}=\left(7^3\right)^{100}=343^{100}\)

Vì \(243< 343\)

Nên \(243^{100}< 343^{100}\)

Vậy \(3^{500}< 7^{300}\)

Answer 2

[trần đức thuận]

tthấy cách này dễ hơn :

(2²⁰¹⁶+2²⁰¹⁷+2²⁰¹⁸):(2²⁰¹⁴+2²⁰¹⁵+2²⁰¹⁶⁾

=2²⁰¹⁶.(1+2+2²):2²⁰¹⁴.(1+2+2²)

=(2²⁰¹⁶.7)+(2²⁰¹⁴.7)

=2²

⁼⁴