My approach: Rewrite 100^50 = (10^2)^50 = 10^100. Then (50^100)/(100^50) = (50^100)/(10^100) = (50/10)^100 = 5^100. Which is of course the same as 25^50 = (5^2)^50 = 5^100.
Since 100^50=(2*50)^50=2^50*50^50, 50^100/100^50=50^(50+50)/(2^50*50^50)=50^50/2^50=(50/2)^50=25^50 Since 25=5^2, we can rewrite this resulllttt also to 25^50=(5^2)^50=5^(2+50)=5^100
My approach:
Rewrite 100^50 = (10^2)^50 = 10^100.
Then (50^100)/(100^50) = (50^100)/(10^100) = (50/10)^100 = 5^100.
Which is of course the same as 25^50 = (5^2)^50 = 5^100.
Mistake at 3:52 , you put down an extra zero.
5^100
Since 100^50=(2*50)^50=2^50*50^50, 50^100/100^50=50^(50+50)/(2^50*50^50)=50^50/2^50=(50/2)^50=25^50
Since 25=5^2, we can rewrite this resulllttt also to 25^50=(5^2)^50=5^(2+50)=5^100
problem
( 50 )¹⁰⁰ / (100)⁵⁰ = ?
( 50 )¹⁰⁰ / (100)⁵⁰ = ( 5• 10 )¹⁰⁰ / (100)⁵⁰
= ( 5 ¹⁰⁰• 10 ¹⁰⁰ ) / (100)⁵⁰
= ( 5 ¹⁰⁰• 10 ⁽²⁾ ⁽⁵⁰⁾ ) / (100)⁵⁰
= ( 5 ¹⁰⁰• (10 ⁽²⁾)⁽⁵⁰⁾) / (100)⁵⁰
= ( 5 ¹⁰⁰• (100)⁵⁰ ) / (100)⁵⁰
= 5 ¹⁰⁰
A 70 digit decimal number!
answer
5 ¹⁰⁰
Yes, I think 5^100 is better than 25^50.