Those Are Big Numbers!

Using the Rules of Exponents , we can write:

$\color{#D61F06}{25^{100} = (5^2)^{100} = 5^{200}}$ .

$\color{#3D99F6}{2^{600} = 2^{3\cdot 200} = (2^3)^{200} = 8^{200}}$ .

$\color{#20A900}{3^{400} = 3^{2\cdot 200} = (3^2)^{200} = 9^{200}}$ .

Now we can easily compare them!

$\color{#20A900}{9^{200}} > \color{#3D99F6}{8^{200}} > \color{#D61F06}{5^{200}} > \color{#69047E}{4^{200}}$

so $C>B>A>D.$

3^4> 2^6> 25^1> 4^2; So C > B > A > D

A = 25¹⁰⁰ = 5²⁰⁰

B = 2⁶⁰⁰ B = 2²⁰⁰.2²⁰⁰.2²⁰⁰ or B = D.2²⁰⁰ :: B > D

C = 3⁴⁰⁰ = 3²⁰⁰.3²⁰⁰ ; 3.3 > 5 :: 3²⁰⁰.3²⁰⁰ > 5²⁰⁰ :: C > A

if 2.2.2 < 3.3 then 2²⁰⁰.2²⁰⁰.2²⁰⁰ < 3²⁰⁰.3²⁰⁰ or B < C

D = 4²⁰⁰ = 2⁴⁰⁰ :: D < A

B > D C > D A > D
B > A B > C
C > A ::

C > B > A > D