Question

So sánh:

a) 243⁷ và 9¹⁰ . 27⁵

b) 15¹⁵ và 81³ . 125⁵

c) 78¹⁵ - 78¹² và 78¹² - 78⁹

Answer 1

a) \(243^7\) và \(9^{10}.27^5\)

\(243^7=\left(3^5\right)^7=3^{35}\\ 9^{10}.27^5=\left(3^2\right)^{10}.\left(3^3\right)^5=3^{20}.3^{15}=3^{35}\)

Vì: \(3^{35}=3^{35}\) nên \(243^7=9^{10}.27^5\)

b) \(15^{15}\) và \(81^3.125^5\)

\(15^{15}=\left(3.5\right)^{15}=3^{15}.5^{15}\\ 81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{12}.5^{15}\)

Vì: \(3^{15}.5^{15}>3^{12}.5^{15}\) nên \(15^{15}>81^3.125^5\)

 

Answer 2

c) \(78^{15}-78^{12}=78^{12}.78^3-78^9.78^3=78^3\left(78^{12}-78^9\right)\)

\(78^{12}-78^9=78^0.78^{12}-78^0.78^9=78^0\left(78^{12}-78^9\right)\)

Vì: \(78^3>78^0\) nên \(78^{15}-78^{12}>78^{12}-78^9\)