Which is larger: 2^500 or 5^200?

  • Thread starter Icelove
  • Start date
In summary, the question asks whether 2^500 or 5^200 is bigger. By simplifying the expressions, it can be shown that 2^500 is bigger. This can be proven by dividing the two numbers and using the fact that a/b^n is greater than 1/a.
  • #1
Icelove
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Homework Statement


Which is bigger 2^500 or 5^200


Homework Equations


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The Attempt at a Solution


Well I got to 2^2^250 -> 4^250 vs 5^200... by the looking at it 4^250 is bigger but I can't just say it looks bigger... There are lots of these that I can't get on a common base, so if anyone can point me to the right direction I'll give lots of love.
 
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  • #2
divide the two numbers.
come to a form of (a/b^n)^k * a^k = (a*(a/b^n))^k
prove that a/b^n > 1/a
from that you can easily proove that the numerator is bigger than the denominator
 

FAQ: Which is larger: 2^500 or 5^200?

How do you determine which is bigger between two numbers?

The easiest way to determine which number is bigger is by comparing them using the greater than (>) and less than (<) symbols. The number on the left of the symbol is always considered the smaller number, while the number on the right is considered the bigger number.

Can you use a calculator to determine which number is bigger?

Yes, you can use a calculator to determine which number is bigger. Simply enter the two numbers and use the greater than (>) and less than (<) symbols to compare them. The calculator will display the result indicating which number is bigger.

How do you determine which is bigger between fractions?

To determine which fraction is bigger, you can convert them into decimal form and then compare them. You can also find a common denominator and compare the numerators. The fraction with the larger numerator will be the bigger fraction.

What if the numbers have different units?

If the numbers have different units, you can convert them into the same unit before comparing them. For example, if one number is in inches and the other is in centimeters, you can convert the inches into centimeters or vice versa before comparing them to determine which is bigger.

Is there a way to determine which number is bigger without using the greater than and less than symbols?

Yes, you can also determine which number is bigger by subtracting one number from the other. If the result is a positive number, then the number being subtracted is bigger. If the result is negative, then the number being subtracted is smaller. If the result is zero, then the numbers are equal.

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