Math Olympiad Question | Compare 100^99 and 99^100 which is larger?

We're trying to figure out whether 100^99 or 99^100 is bigger, it's like comparing two super-sized piles of candies to see which one has more.

Think about 100^99 as 100 multiplied by itself 99 times, that’s a lot of multiplication! Now imagine 99^100, which is 99 multiplied by itself 100 times. It's like having one more group of candies in the second pile.

Let’s compare these two numbers using smaller examples to see what happens:

• If we take 2^3 (which is 8) and compare it with 3^2 (which is 9), 3^2 ends up being bigger.
• Try another one: 4^5 = 1024, while 5^4 = 625, again, the second number wins.

This pattern often happens when the base number is smaller but gets multiplied more times. In our big example, even though 99 is slightly less than 100, it’s multiplied one extra time (100 times vs 99 times), giving 99^100 a slight edge.

So, 99^100 ends up being the bigger number, like having just a little more candy in your pile! We're trying to figure out whether 100^99 or 99^100 is bigger, it's like comparing two super-sized piles of candies to see which one has more.

Think about 100^99 as 100 multiplied by itself 99 times, that’s a lot of multiplication! Now imagine 99^100, which is 99 multiplied by itself 100 times. It's like having one more group of candies in the second pile.