Tricky Math Olympiad Question | You should know this!

[00:00:00]Hi guys, here we have an interesting math Olympiad question. It says 16 ^ 5 - 16 ^ 4 equals what? So how we going to solve this? The first step what we going to do here is take 16 as 2 to the^ of 4. Then we have power of 5 minus again 16 can be written as 2 ^ 4 over 4.

[00:00:30]Now this is same as 4 * 5 is 20. So 2 ^ 20 - 2 ^ 4 * 4 gives us 16. Now you have 2 ^ 20. 20 can be written as 16 + 4, right?

[00:00:51]16 + 4 and here we have 2 ^ 16.

[00:00:56]So this can be split up into 2 ^ 16 * 2 ^ 4. Same base multiplication you add the powers 16 + 4 right then we have - 2 ^ 16.

[00:01:11]After this step if you see there's 2 to the^ of 16 here and here as well. So we take it out common. So in our next step 2 to the^ 16 is out inside what is left is divide 2 ^ 16 * 2 ^ 4 / 2 ^ 16. So you're left with 2 ^ 4 - 2 ^ 16 / 2 ^ 16 we get 1. All right. Next we have 2 ^ 16 2 ^ 4 is how much? 2 * 2 4 4 * 2 8 8 * 2 16 - 1. Then again we have 2 to the^ of 16. Inside the bracket 16 - 1 is 15.

[00:02:05]You have now 2 to the^ of 16 can be written as 10 + 6.

[00:02:13]Right? And then you have * 15 and that's equal to again we're just going to split up 2 ^ 10 * 2 ^ 6 * 15.

[00:02:27]All right. So now we know what is 2 ^ of 10 that's just equal to 1,24.

[00:02:37]Then you have * 2 to the^ of 6 is 64 * 64 * what do we have? 15 right? So you have 1,024 * 64 * 15.

[00:02:53]Now let's solve this. So you have 1,24 * 64.

[00:03:03]All right. 15 can be written as 10 + 5.

[00:03:10]All right. Then 1,024 * 64 * 10 will give you 640.

[00:03:20]Then you have + then you have 64 * 5.

[00:03:27]So * 5 is this is 64 * 10. So * 5 will be half of 640. So that's just 320.

[00:03:39]Next you have 1,024.

[00:03:44]Then this is inside the bracket. 640 + 320 gives 0 + 0 0. 4 + 2 is 6. 6 + 3 is 9. So you have 960.

[00:03:56]So 1,24.

[00:03:58]960 can be written as 1,000 - 40. Right?

[00:04:06]Now multiplying is easy. 1,024 * 1,000.

[00:04:11]So I'll just write three zeros. What we have here? 1 2 3 zeros. Then 1,024 * 1.

[00:04:19]So that will give 1,24,000US [snorts] 40 * 1,024. So, I'm going to write the 0 first. All right.

[00:04:32]0. Then 1,024 * 4. 4 * 4 is 16. 4 * 2 is 8. That gives 9.

[00:04:41]4 * 0 is 0. 4 * 1 is 4. So, you have 1,024.

[00:04:49]3 0 - 40,960 is how much? That's just equal to 0 - 0 0. 10 - 6 is 4. Then you have 9 - 9 again 0. Then you have 4 that becomes 3. 3 - 0 is 3.

[00:05:12]Then you have 2 - 4 that is 12 - 4 8.

[00:05:18]And then this becomes 9. 9 - 0. So you have So you have 983,040.

[00:05:28]So that's your answer. Thank you so much for watching. Bye-bye. again.