Question

Answer 1

Ta có :

`2^120=(2^4)^30=16^30`

`3^90=(3^3)^30=27^30`

`5^60=(5^2)^30=25^30`

Vì `16<25<27`

`=>16^30<25^30<27^30`

`=>2^120<5^60<3^90`

`b)`

`1024=(2^10)^9=2^90`

Vì `2^100>2^90`

`=>2^100>1024^9`

Answer 2

\(a,2^{120}=2^{4.30}=\left(2^4\right)^{30}=16^{30}\)

\(3^{90}=3^{3.30}=\left(3^3\right)^{30}=27^{30}\)

\(5^{60}=5^{2.30}=\left(5^2\right)^{30}=25^{30}\)

\(16^{30}< 25^{30}< 27^{30}\Rightarrow2^{120}< 5^{60}< 3^{90}\)

\(b,1024^9=\left(2^{10}\right)^9=2^{90}\)

\(2^{100}>2^{90}\Rightarrow2^{100}>1024^9\)