Spain Can you solve this Math Olympiad Question

[00:00:00]Hi guys, how are you all? I have an interesting math Olympia question. It says 7 to the power of 5 + 7 to the power of 4 + 7 cubed + 7 squared + 7 to the power of 1 equals what? How are going to solve this?

[00:00:15]I have a very easy solution for this.

[00:00:19]Without using calculators, we're going to solve this. So, what is the first step we're going to do here is You can see 7 to the power of 5, right?

[00:00:27]So, we're going to break down this into 7 to the power of 4 * 7 to the power of 1.

[00:00:36]All right? Because 7 to the power of 4 + 1 will give you 5. Okay.

[00:00:43]The next one I have 7 to the power of 4, so I'm going to write it like that only.

[00:00:48]Plus, then I have 7 cubed, right? 7 cubed can be written as 7 squared * 7 to the power of 1 because 2 + 1 makes it 3.

[00:01:01]Plus, I have 7 squared plus 7 to the power of 1.

[00:01:08]All right? That's it. Now, what I'm going to do here is you have 7 to the power of 4 here and 7 to the power of 4 here. So, we're going to just take that out common.

[00:01:22]Okay? 7 to the power of 4 is out now.

[00:01:27]Now, this part 7 to the power of 4 * 7 to the power of 1 / 7 to the power of 4 equals what? Only this, right?

[00:01:36]7 to the power of 1.

[00:01:38]Plus 7 to the power of 4 / 7 to the power of 4 is equal to 1.

[00:01:45]So, we're left with 1 here.

[00:01:47]Plus Here I have 7 squared and 7 squared, so we're going to take that out. 7 squared common.

[00:01:56]What am I left with? Here 7 squared * 7 to the power of 1 / 7 squared. So, we are left with 7 to the power of 1.

[00:02:06]Plus, 7 squared / 7 squared, you have 1.

[00:02:10]Plus, what do I What do I have here? 7 to the power of 1.

[00:02:15]Perfect. Next.

[00:02:18]We have 7 to the power of 4.

[00:02:22]Next, inside the bracket, what do we have? 7 to the power of 1 is 7. 7 + 1 is 8.

[00:02:29]Plus, I have 7 squared here. So, I'm going to write that. Then, inside the bracket, I have 7 to the power of 1.

[00:02:37]That is 7. Plus 1, again, 8.

[00:02:41]Plus, I have 7 to the power of 1.

[00:02:45]Perfect.

[00:02:47]Okay. What we do in our next step is Here, you have 8. Here, you have 8.

[00:02:57]So, can I take that out common? Right?

[00:02:59]8. Okay. Inside the bracket. This whole part divided by 8. So, what am I left with?

[00:03:06]7 to the power of 4.

[00:03:09]Plus, 8 * 7 squared / 8. Am I left with? 7 squared.

[00:03:17]So, 7 squared. Plus, 7 to the power of 1 is 7.

[00:03:22]Perfect.

[00:03:24]Next step.

[00:03:26]8 times 7 to the power of 4 can be written as 7 squared * 7 squared.

[00:03:36]Plus, we have 7 squared.

[00:03:39]Right? Because 2 + 2 makes 4.

[00:03:41]Plus, you have 7.

[00:03:44]Next step.

[00:03:46]See here.

[00:03:48]7 squared, 7 squared, you can take 1 7 squared out, right? Common. So, what are you left with?

[00:03:54]This 7 squared * 7 squared / 7 squared.

[00:03:58]You're left with 7 squared.

[00:04:01]Plus this part, 7 squared / 7 squared, 1.

[00:04:05]And here you have eight. So, that eight I'm going to write.

[00:04:09]Plus you have seven.

[00:04:11]Done? Okay.

[00:04:13]What is 7 squared?

[00:04:15]49.

[00:04:17]Times 7 squared is 49 + 1 is 50.

[00:04:21]Then you have eight plus seven.

[00:04:26]Next, what do we do?

[00:04:27]You have 49.

[00:04:30]49 can be written as 50 - 1.

[00:04:35]And here you have 50 * 8 + 7.

[00:04:43]Next.

[00:04:44]This is 50 - 1, right? 50 * 8 is what?

[00:04:49]That's 400.

[00:04:51]Plus seven.

[00:04:53]Next.

[00:04:55]50 * 400 is how much?

[00:04:59]You have 1 2 3 0s, so I'm going to write that.

[00:05:02]1 2 3 0s.

[00:05:05]5 * 4 is 20.

[00:05:07]So, 20,000 - 1 * 400 is - 400.

[00:05:14]Plus you have seven.

[00:05:17]Done?

[00:05:18]Okay.

[00:05:19]Next.

[00:05:21]We just have to subtract 20,000 - 400.

[00:05:24]How much is 20,000 - 400? See these two 0s, I'm going to write that down. Two 0s.

[00:05:31]200 - 4 is how much?

[00:05:34]196.

[00:05:37]19600 plus seven.

[00:05:42]So, your answer is 19,607.

[00:05:50]This is how we found the answer without using a calculator. Isn't it amazing?

[00:05:55]Thank you so much for joining. Bye-bye.

[00:05:57]Take care.