Why Everyone Gets This 6th Grade Math Problem Wrong

Added: 2026-05-06

[00:00:00]Hi everyone. I'm looking at this math equation and I'm trying to see how how how do we get four because four is a low number and if so I'm thinking of a low number two right for X. I'm guessing here. So let's say X is one. So 8 * 2 is 16. So I'm trying to figure out how how did how how do we get four?

[00:00:25]Hmm. Okay, let's do this.

[00:00:28]Let's rewrite eight as a power because we're looking at a power here of X.

[00:00:34]Sorry. You got a power. Yes, you got a a base and an exponent. So that's a power.

[00:00:40]So let's rewrite this eight as a power as well. So two to the third, right? 2 * 2 is 4 * 2 is 8 * 2 to the X = 4. Let's write that four as a power as well to keep all the bases the same. All the twos, let's keep all twos. So it'll be 2 to the 2. 2 * 2 is 4. And now we're looking at this. And let's let's let's make sure that we have 2 to the X by itself. So we're going to divide.

[00:01:16]So we'll do this. These cancel out and write it here. That's not a 23.

[00:01:23]That's a 2 to the third. 2 to the third.

[00:01:27]And I'll write here 2 to the X = So this we're dividing.

[00:01:36]Basic the the base are the same. So we just subtract. So it'll be two the same.

[00:01:46]So it'll be 2 - 3 which is -1.

[00:01:54]So 2 to the X = 2 to the -1.

[00:02:02]And because the bases are the same on both sides that means that the exponents must be the same. So it's like a mirror.

[00:02:14]So let's let's check it out and see. So we'll we'll um enter this -1 into the X. So X is -1.

[00:02:25]And I am going to write that up here to the top right corner of the board. So X = -1. Let's test that out and see if that's correct. So we have 2 to the third * 2 to the -1 = 2 to the 2.

[00:02:50]Okay. So anytime you're multiplying So anytime you're multiplying uh two powers, so we we have the bases are the same. We're multiplying the same base.

[00:03:03]You add the exponents and there's a rule. It's this. So A * A = A.

[00:03:12]So exponent M * N = M + N. So you're adding your your exponents, but you're keeping the same base because hey, we got the same base here. So two, we keep the same base and it's 3 + -1.

[00:03:38]Right?

[00:03:40]That = 3. It's the same. So it's the same as 3 - 1. So it'll be 2.

[00:03:47]And that = 2. So that's 4 = 4. So that's true. Now let's see if it works the the the the the 8 * 2 X = 4. Let's see if that works. So 8 * 2 to the -1 = 4. So we have eight. Let's write that in a fraction form to make the math fun and easy. 8 over 1 = 8. Does not change the eight. * and then we're going to There's a rule. If if you want to turn this into a fraction, this two -1, there is a rule.

[00:04:32]It's this. So anytime you have a negative exponent oh, it's negative M.

[00:04:39]It you write the reciprocal. So it'll be 1 over A M.

[00:04:46]So it it you turn that exponent to a positive. So A M. That's an M.

[00:04:54]All right. So we'll do the same thing here. The reciprocal of two to the one -1 will be 1 over right?

[00:05:07]2 to the 1.

[00:05:10]So we turn that negative exponent to a positive one.

[00:05:17]And then we just multiply across. So 8 * 1 is 8 over 1 * 2 is 2. And then you divide. 8 / 2 is 4.

[00:05:30]And there you go. So it does work. And so X is -1.

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