[tex]\it a)\ 4^2>8;\ \ 4^2=16>8\\ \\ b)\ \ 10^3=1000;\ \ 10^3=10\cdot10\cdot10=1000\\ \\ c)\ \ (3^5)^4>(3^2)^8;\ \ (3^5)^4=3^{20}>3^{16}=(3^2)^8\\ \\ d)\ \ 9^{75}=27^{50};\ \ 9^{75}=(3^2)^{75}=3^{150}=(3^3)^{50}=27^{50}\\ \\ e)\ \ 125^5<25^8;\ \ 125^5=(5^3)^5=5^{15}<5^{16}=(5^2)^8\\ \\ f)\ \ 2^{30}<3^{20};\ \ 2^{30}=(2^3)^{10}<(3^2)^{10}=3^{20}\\ \\ g)\ \ 3^{120}<1000^{20};\ \ 3^{120}=(3^6)^{20}=729^{20}<1000^{20}\\ \\ h)\ \ 2^{33}<3^{23}[/tex]
[tex]\it \left.\begin{aligned}\it 2^{30}<3^{20}\ \ din\ f)\ \\ \\ \it 2^3<3^3\end{aligned}\right\} \Rightarrow 2^{30}\cdot2^3<3^{20}\cdot3^3 \Rightarrow 2^{33}<3^{23}[/tex]
