Without using a calculator how can we say 6^20> 3.10^8?

Question

Please help me understand the method you are using.

Answer 1

And one more :

$6^{20}=(6^2)^{10}= (36)^{10} > (3 \cdot 10)^{10}=$

$3^{10}10^{10} >3×10^8.$

Answer 2

$6^{20}=6^{4}6^{8}6^{8}>6^{4}2^{8}5^{8}=6^{4}10^{8}>(3)10^8$

Also, if there were meant to be parentheses: $$6^{20}=(6^2)^{10}=36^{10}>30^{10}>30^{8}$$

Answer 3

Note that

$$2^{10}=1024>1000=10^3$$

then

$$6^{20}=3^{20}2^{20}>2^{20}2^{20}=2^{40}=(2^{10})^4>(10^3)^4=10^{12}$$

Answer 4

$$6^{20}=(2\cdot3)^{20}=2^{20}\cdot 3^{20}=2^{20}\cdot {(3^5)}^4=2^{20}\cdot {243}^4\gt2^{20}\cdot {200}^4=2^{20}\cdot (2\cdot 100)^4=2^{20}\cdot 2^4\cdot 100^4=2^{24}\cdot {(10^2)}^4=2^{24}\cdot 10^8\gt3\cdot 10^8$$