Olympiad Mathematics | A tricky Algebra problems solution without Calculator |

Ajouté : 2026-05-26

[00:00:00]Hello everyone. Welcome to Russell's Classroom. Today we are simplifying a interesting math question without calculator.

[00:00:08]Which is 4 to the power 3, 3 to the power 2, 2 to the power 1 minus 1 2 3 4 is equal to what?

[00:00:15]So how to simplify this interesting math question without calculator?

[00:00:21]So first of all, I take our question.

[00:00:24]Which is 4 to the power 3.

[00:00:29]Then which is 2 to the power 1.

[00:00:32]Minus 1 2 3 4. This is our question.

[00:00:37]So at this moment, you can say this is 2 to the power 1, which is 2.

[00:00:43]So it will be 4 to the power 3.

[00:00:46]Then 2 to the power 1, which is 2. Minus 1 2 3 4.

[00:00:54]Now in this expression, this is 3 to the power 2. So you know that 3 to the power 2, which is 3 * 3.

[00:01:03]Which is 9. So 3 to the power 2, this is 9. So this 3 to the power 2, it will be 9. So this expression, it will be 4 to the power 9.

[00:01:14]Minus 1 2 3 4.

[00:01:19]Now.

[00:01:20]This is 4.

[00:01:22]So you know that 4, it will be 2 to the power 2. 2 to the power 2, this is 4.

[00:01:27]But this exponent, it will be 9. And minus 1 2 3 4.

[00:01:35]Then.

[00:01:37]At this moment, you can say if I apply this math formula here, A to the power N and all to the power M.

[00:01:44]Which is A to the power NM.

[00:01:48]So this 2 * 9, it will be 18.

[00:01:50]So this expression, it will be 2 to the power 18.

[00:01:56]Minus 1 2 3 4 Now, this is 2 to the power 18. So, 2 to the power 18 you can say that it will be 2 to the power 8 plus 10. 8 + 10 this is 18 minus 1 2 3 4 Then, this is 2 to the power 8 If I separate this case, we know that a to the power n plus m which is a to the power n times a to the power m If I apply this math formula here, so this expression it will be 2 to the power 8 times 2 to the power 10 minus 1 2 3 4 Then, this is 2 to the power 8. So, 2 to the power 8 is equal to what? So, we know that 2 to the power 8 This is 2 to the power 4 times 2 to the power 4 which is 16 times 16 and it will be 256.

[00:03:07]This is 256. So, you can say that it will be 256 But, 2 to the power 10 it is easy. 2 to the power 10 it will be 1024.

[00:03:20]I take this 1024 here 1 0 2 4 minus 1 2 3 4 Now, this times this and subtract this.

[00:03:34]So, how to solve this interesting case?

[00:03:37]So, at this moment you can say this expression it will be 2 5 6 and this 1024 it will be 1000 plus 20 plus 4. All of that, this plus this plus this, it will be this.

[00:03:57]Then minus 1 2 3 4.

[00:04:04]Then you can say here this 10 this. Here is three zero, so it will be 2 5 6 1 2 3 plus 20 times this so I take one zero here. 256 times two it will be 512 plus four times 256, it will be 1024.

[00:04:35]Bracket and minus 1 2 3 4.

[00:04:41]Now, at this moment, if I add this and this and this value, we will find out it will be four.

[00:04:50]Then 2 plus 2, this is four.

[00:04:53]Then it will be one.

[00:04:55]And this is two and this is six and this is two.

[00:05:00]Then minus 1 2 3 4. Now, if I subtract both we will find out our final answer, which is 260910.

[00:05:15]This is our final answer in this math question. We are solving this interesting math question without calculator, which is 4 to the power 3 2 to the power 2 power 1 minus 1 2 3 4 is equal to 260 and 910.

[00:05:37]This is our answer. Thank you all if you enjoy this math problem.

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[00:05:45]Take care everyone.