<p>This is a quantitative comparison problem</p>
<p>Column A: 10^25
Column B: 5^50</p>
<p>I know how to use a calculator to subtract both of em and all, but i wanted to know what the actual steps were to solve this kind of problem by hand. Any help would be appreciated!</p>
<p>Ok this is how I would work it out. I wold break down to simpler steps. I would change 10^25 as (10^5)^5 and I would change 5^50 to (5^10)^5. Now since the last power is the same on each you can ignore it and just consider 10^5 and 5^10. I would leave 10^5 alone, but 5^10 can change to (5^2)^5. Now both have a power of 5 so you can just consider 10 to 5^2, so 10 is less than 25, so 5^50 is the greatest! Someone check my work but I believe thats it!</p>
<p>To solve without a calculutor, convert 10^25 to 5^25<em>2^25 and make 5^50 into 5^25</em>5^25. Now since both sides have 5^25, you can cancel that out and you are left comparing 2^25 and 5^25, of which the latter is obviously larger</p>
<p>(5^2)^25 is the same thing as 5^50. 5^2 is 25, so then you have 25^25, which is greater than 10^25.</p>
<p>Wow.. three different ways to solve the same problem!</p>
<p>Mine is obviously the most correct! ;)</p>
<p>thx a lot guys</p>