This exponential math question looks easy until you try it.

JJ ONLINE MATHS CLASS
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At first glance, x^(x³) = 36 looks simple. But once you start solving, you will see why indices, powers, and logarithms are important. Follow the explanation.
#exponents #maths #algebra #harvard
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Video Summary
AI GeneratedThis video provides a step-by-step mathematical tutorial on how to solve a complex exponential equation. The instructor demonstrates how to manipulate exponents using specific algebraic laws to isolate the variable $x$, ultimately proving the result through substitution to ensure accuracy.
This is easy but very tricky because if you don't know your way around it
Definitely you're going to get stuck, welcome back to my channel. So this is JJ, and we are here.
To solve another amazing exponential multiplication, come on, let's do this together.
Okay, first things first, let's try to find a way to simplify this side and this side.
Okay, or make both of them look alike in any case so that we can equate them. First things we are
What we're going to do is cube both sides; let's cube both sides of the equation, okay? Let's cube both sides.
so what we are going to have is x raised to the power of x raised to the power of three, all cubed
is equal to 36 to the power of three, yeah, I know what you're thinking, you're thinking I'm
increasing this instead of trying to reduce it. Don't worry, we are getting somewhere now. Let us
recall that a to the power of m raised to the power of n is also equal to a to the power of m times n
All right, and this is also equal to a to the power of n raised to the power of m. Now how is
This is going to help us before that, if this is the first time you've seen this amazing channel
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turning at your convenience, there was something new for you to watch, give us a thumbs up if you
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Now when you look at this, I want to make use of this one, this one in this case; now our a is this x.
our n is x cubed and our m is three, so that means that I can write a to the
The power of m to the power of n is also equal to a to the power of n to the power of n, so I'm going
to write this as a to the power of m raised to the power of n, so I'll now write a as x to the power of
of m right and our m is three, okay. Now everything, now raise the power of n, we are using this and.
What is our n? Our n is x to the power of three. I hope I didn't confuse you. Here all we did is we
Used this and this, so this is already in this form; we are changing it to this—that's all now.
This is equal to 36,343. All right, now there is something we need to look at here because I'm
trying to find a way to make this place and this place the same, all right, recall that 36
is the same thing as six multiplied by six, which is the same thing as six squared, so we are going to
Replace this with this, so now we have x to the power of three, raise the power of x to the power.
Three is equal to six squared. Let's report it: we are going to prove that the answer we obtained
It's correct, so try to watch to the end and see whether the answer we obtained is actually correct or not.
now we have to remember that a to the power of m raised to the power of n is equal to a to the
power of m times n, so it simply means that we can rewrite this as x to the power of m times n.
three raised to the power of x raised to the power of three is equal to six raised
to the power of two times three, so we write x to the power of three raised to the power of x
The power of three is equal to six to the power of two times three, which is six. Now remember I said we
We're going to prove that our answer is correct, so I'll extend to six periods and see how we did.
that subscribe to our channel if you have not already, so you don't miss our videos, okay? Now, by
By comparison, we can see that x cubed is equal to six, since we have x to the
three raised to the power of x raised to the power of three is equal to six raised to the power of
six, so it simply means that x to the power of three is equal to six. Now how do we get our x?
Since the question says we should find x, we are going to take the cube root of both sides. Okay, take the cube root of both sides.
so we have the cube root of x raised to the power of three equals the cube root of six, so this and
Here we go, we now have x is equal to the cube root of six, or we can write this as six to the power of one-third.
One over three. Now it's time to show whether our answer is correct or wrong if we have an external
Truth. So let's substitute; we got our x to be six to the power of three, so we have six to the power
one over three raised to the power of six raised to the power of one over three raised to the power
Of three right now is this actually equal to 36? Now the first thing we are going to do is recall
that a to the power of m raised to the power of n is equal to a to the power of m times n, right
so we can write this as six to the power of one over three raised to the power of six to the power
of this becomes one over three multiplied by three over one, right? This times this. Now, is this actually
Equal to 36, we're almost there. If you watch this to the end, please give me a thumbs up in the comments.
That will show me the people who actually watched up to this point, and I appreciate you.
Especially okay, now we look at this; we have three, we take away three, right? So now we have six.
to the power of one over three raised to the power of six — is this actually equal to 36?
now applying the same rule that we applied here, we are going to have six to the power of one over
three multiplied by six over one now is this equal to 36 so we have six to the power of
Three we divide six to give us two, so now we have six to the power of two remaining, okay? Is this
equal to 36, and yes, six squared is actually 36; this is equal to 36, and that proves that the
The answer we received is correct. Thank you so much for watching, and I'll see you in my next video.
