a )
Ta có :
\(125^3=\left(5^3\right)^3=5^9\)
Do \(5^9< 5^{10}\)
\(\Rightarrow125^3< 5^{10}\)
b )
Ta có :
\(222^{333}=\left(222^3\right)^{111}\)
\(333^{222}=\left(333^2\right)^{111}\)
So sánh : \(222^3;333^2\)
Lại có :
\(222^3=\left(2.111\right)^3=2^3.111^3=8.111^3=8.111.111^2=888.111^2\)
\(333^2=\left(3.111\right)^2=3^2.111^2=9.111^2\)
Do \(888.111^2>9.111^2\)
\(\Rightarrow222^3>333^2\)
\(\Rightarrow\left(222^3\right)^{111}>\left(333^2\right)^{111}\)
\(\Rightarrow222^{333}>333^{222}\)
~ Ủng hộ nhé
a,
Ta có :
1253 = ( 53 )3 = 53.3 = 59 < 510
=> 510 > 1253
a ) Ta có :
1253 = ( 53 )3 = 59
Mà 59 < 510 Do đó 510 > 1253
Vậy 510 > 1253
b ) Ta có
222333 =( 2223 )111 = ( 1113 . 23 )111 = ( 1112 . 888 )111
333222 = ( 3332 )111 = ( 1112 . 32 )111 = ( 1112 . 9 )111
Mà ( 1112 . 888 )111 > ( 1112 . 9 )111 Do đó 222333 > 333222
Vậy 222333 > 333222
a, Ta có : \(125^3=\left(5^3\right)^3=5^9\)
Vì \(5^{10}>5^9\Rightarrow5^{10}>125^3\)
b, Ta có : \(222^{333}=\left(222^3\right)^{111}\)
\(222^3=\left(2\cdot111\right)^3=2^3\cdot111^3=8\cdot111\cdot111^2=888\cdot111^2\)
\(333^{222}=\left(333^2\right)^{111}\)
\(333^2=\left(3\cdot111\right)^2=3^2\cdot111^2=9\cdot111^2\)
Vì \(888\cdot111^2>9\cdot111^2\)\(\Rightarrow222^3>333^2\)\(\Rightarrow222^{333}>333^{222}\)
