Only 10% Students Solve this exponential math olympiad question | X^1250 =5^X^2 |

Added: 2026-05-30

[00:00:00]Hello everyone. Welcome to Rafa's Classroom. Today we are solve a interesting exponential math problem, which is x to the power 1 2 5 0 is equal to 5 to the power x to the power 2. X is equal to what? How to solve this interesting exponential math problem?

[00:00:20]I solve this question easy method our math solution.

[00:00:27]Our question which is x to the power 1 2 5 0 is equal to 5 to the power x to the power 2. This is our question.

[00:00:42]Now, first of all, I can easily this expression, it will be x to the power This is it will be 2 * 6 2 5 is equal to 5 to the power x to the power 2.

[00:00:59]Now, all of that the exponential formula a to the power m n, which is a to the power m whole to the power n.

[00:01:10]If I apply this exponential math formula, this expression it will be x to the power 2 bracket whole to the power 6 2 5 is equal to 5 to the power x to the power 2.

[00:01:28]Now, this is x to the power 2, this is x to the power 2.

[00:01:31]So, at this moment, let x to the power 2 is equal to m.

[00:01:39]Now, I substitute this value here. So, it will be m to the power 6 2 5 is equal to This is 5 to the power m.

[00:01:53]Now, I use both side exponent 1 over m.

[00:01:57]So, this exponential expression it will be M to the power 625 bracket whole to the power 1 over M is equal to 5 to the power M bracket whole to the power 1 over M.

[00:02:15]Now, this expression it will be M to the power 625 times which is 1 over M is equal to this is 5 to the power M times 1 over M.

[00:02:32]Now, this M this M is cancel out.

[00:02:36]We are find out which is M to the power 625.

[00:02:42]This time this it will be this over this M is equal to 5.

[00:02:49]Now, at this moment I again I use again both side exponent which is M to the power 625 over M bracket whole to the power 1 over 625 is equal to 5 to the power 1 over 625. I use both side exponent 1 over 625.

[00:03:17]Now, this time this so it will be M to the power 625 over M times 1 over this is 625 is equal to 5 to the power 1 over 625.

[00:03:35]Now, this 625 this 625 is cancel.

[00:03:39]We are find out which is M to the power 1 over M is equal to 5 to the power 1 over 625.

[00:03:51]Now, how to find out the value of m in this exponential expression?

[00:03:58]Let me explain. At this moment, I can say easily this expression, it will be m to the power 1 over m is equal to 5 to the power 1 times this is 1 over 625.

[00:04:18]Then this is m power is 1 over m is equal to this expression, it will be 5 to the power 5 over 5. Oh, no, that 5 divide 5, this is 1 times here is exponent 1 over 625.

[00:04:37]Now, this is m to the power 1 over m then this expression, you can say it will be 5 to the power 5. I take this 5 here, bracket whole to the power it will be 1 over this 5 here times this exponent will be 6 2 5.

[00:04:58]Now, in this expression, m to the power 1 over m is equal to 5 to the power 5 is equal to what? How to simplify this expression?

[00:05:09]So, 5 to the power 5, you can say easily it will be 5 to the power 2 times 5 to the power 2 times 5.

[00:05:17]This is 25 and this is 25. So, 25 times 25, it will be 625. 625 times 5, it will be 3,000 125.

[00:05:34]Now, at this moment, you can say this is 300 1,025.

[00:05:40]Then this is 1 and this 5 times 625, this is 3,000 Now, at this moment, if I compare both, at this moment, you can easily hear m is equal to 300 3,000 125.

[00:06:04]Now, remember that I recall m is equal to x squared. I substitute this value here. So, m is equal to x squared. So, I take this value here. I take I get x is equal to what? So, this is x to the power 2 is equal to 3 1 2 5.

[00:06:24]Then, I use both side square root, so which is x to the power 2 bracket square root, then here is a square root 3 1 2 5.

[00:06:36]Then, at this moment, this squared is cancelled. We are find out it will be x, and this is plus minus.

[00:06:43]And this x especially it will be 25 * 25 * 5.

[00:06:51]Now, this is x, and this is plus minus, and it will be square root 25.

[00:06:59]* square root 25. I I separate this case and a square root 5.

[00:07:05]Now, at this moment, you can say here x is equal to plus minus.

[00:07:11]This is square root 25, which is 5 * square root 25, it will be 5 * and this is a square root 5.

[00:07:21]Then, this is x [clears throat] is equal to plus minus. 5 * 5, this is 25.

[00:07:29]And this is a square root 5. So, we are find out our final answer, which is x is equal to plus minus 25 whole square root 5. So, our question, which is x to the power 1250 is equal to this is 5 [clears throat and snorts] to the power x to the power 2 here x is equal to plus minus 25 square root 5. This is our final answer in this viral exponential math problem.