Can You Solve This Challenging Exponential Equation?

Added: 2026-05-28

[00:00:01]For us to handle this, let's square both sides of this equation first.

[00:00:07]So, if I square this, the square will affect this three and the square will also affect this six. That is by squaring both sides. So, here 3 squared will give me nine. So, I have 9 to the power A there when I square it.

[00:00:20]And it's equal to when I square that side, I have 36 to the power B.

[00:00:25]Now, the next thing for us to do, I want to remove this A from this power. So, I can simply raise this part to the power 1 over A.

[00:00:36]And I say it's equal to 36 to the power B and then all raised to the power 1 over A.

[00:00:45]So, that this A will cancel A here. So, I'm left with nine is equal to 36 to the power This will be left with B over A because nothing has canceled there. So, B over A.

[00:01:00]Now, in the same way, I want to eliminate B from this power. So, I can raise both sides to the power 1 over B.

[00:01:08]So, I'm going to say 9 to the power A, that is this one, I'm raising it to the power 1 over B is equal to 36 to the power B, 36 to the power B.

[00:01:22]And then I'm also raising it to the power 1 over B.

[00:01:28]So, that 36 can be eliminated. So, sorry, so that the power B can be eliminated. So, B will cancel B.

[00:01:37]And then what I'm left with here is nine to the power A over B.

[00:01:45]Because nothing has canceled here. So, A multiplied by 1 is A over B. And that will be equal to 36. Nothing is left here. So, this is 36 to the power 1, which is the same thing as 36. So, now that we have simplified this, we can now go back to the second part of the equation that says we should evaluate this. So, 36 to the power b over a 36 to the power b over a is equal to 9.

[00:02:11]So, in place of this 36 to the power b over a, I'm going to write 9. So, that will be 9.

[00:02:17]And then here I have minus.

[00:02:19]So, I say minus. Then 9 to the power a over b, 9 to the power a over b, see it here, is equal to 36. So, minus 36.

[00:02:31]And that will finally give me minus 27 as the final answer. Hope you enjoyed this video. Please don't forget to like, share, and join for more videos like this. Thank you for watching.