Question

So sánh:

a) 21¹⁵ và 27⁵.49⁸

b) A= 100⁴⁵- 100⁴⁴ và 100⁴⁴- 100⁴³

Answer 1

a) \(21^{15}=3^{15}\cdot7^{15}\)

\(27^5\cdot49^8=\left(3^3\right)^5\cdot\left(7^2\right)^8=3^{15}\cdot7^{16}\)

vì \(7^{15}< 7^{16}\)

Nên \(3^{15}\cdot7^{15}< 3^{15}\cdot7^{16}\)

Vậy \(21^5< 27^5\cdot49^8\)

Answer 2

b) \(100^{45}-100^{44}=100\cdot100^{44}-100\cdot100^{43}\)

\(=100\left(100^{44}-100^{43}\right)\)

Do đó:\(100\left(100^{44}-100^{43}\right)>100^{44}-100^{43}\)

Vậy \(100^{45}-100^{44}>100^{44}-100^{43}\)