A Harvard University interview algebra math test|No calculator|algebra simplification.

Without a calculator, can you simplify this? Now let's evaluate it together. The first is, we are going to express 5 in terms of 4. And 5 in terms of 4 is 4 plus 1, right? So we'll write this as 8 raised to the power of 4 plus 1, plus 8 raised to the power of 4, plus... Now, 3 in terms of 2 is 8 to the power of 2 plus 1, plus 8 to the power of 2. then plus 8 to the power of 1 plus 1 equals what? Okay? Now, we have... Remember that 8 raised to the power of m plus n is equal to 8 raised to the power of m multiplied by 8 raised to the power of n. That means we can write this as 8 raised to the power of 4 multiplied by 8 raised to the power of 1, plus 8 raised to the power of 4. Now, this can be written as 8 squared multiplied by 8 to the power of 1, plus 8 squared. 8 to the power of 1 is 8, plus 1 is equal to what? Now, remember that 8 to the power of 0 is 1. I forgot to mention that because any number raised to the power of 0 is 1. Alright, now that we have the same expression here and here, we can factor that out. So if we do that, we have 8 to the power of 4 brackets. When this is divided by this, 8 to the power of 1 will remain. So we have 8 to the power of 1 plus... 8 to the power of 4 divided by itself equals 1. So we have 1 plus... Here, we bring out 8 to the power of 2, right? Now, when this is divided by 8 squared, 8 will remain. And when this is divided by itself, 1 will remain. So we have 8 to the power of 1 plus 1, plus 8 plus 1 equals 9. Now, this is equal to 8 raised to the power of 4 multiplied by 8 plus 1, which is 9. Eight to the power of 2 multiplied by 8 plus 1 is 9. Plus nine, alright? Now, you can see that we have 9, 9, 9 here. They are common factors. So we are going to factor that out. Now, let's factor out 9. So this is equal to 9 brackets. When this is divided by 9, we get 8 raised to the power of 4. 8 to the power of 4 plus... When this is divided by 9, the remainder will be 8 squared. 8 to the power of 2 plus... When 9 is divided by itself, 1 remains. Alright? Now, this is equal to 9 brackets. Now, 8 to the power of 4... Remember that we are doing this without a calculator. So we're going to solve this, simplifying it as much as possible. Click the subscription button and turn on the notification bell. If this is the first time you are encountering our video. Yes, so you'll be notified every time we upload our videos. We upload videos daily, 2 to 3 times per day. So always tune in at your convenience to watch our latest upload. And please, give us a thumbs up if you're actually enjoying this video. Thank you very much. 8 to the power of 4 is the same thing as 8 to the power of 2 plus 2, right? So we have this as 8 squared plus 2. Alright? 8 squared plus 1. Alright? Now, this is equal to 9 brackets. Remember, using the same law that we used here. We are going to express this as 8 squared multiplied by 8 squared. So we have 8 squared multiplied by 8 squared. 8 squared plus 1. Okay? So we have this to be equal to 9 brackets. 8 to the power of 2 brackets. Let's factor that out. Let's use a different type of bracket here. Alright. Now, when this is divided by this, one will remain, right? So 8 to the power of 2 will remain. Moreover, when this is divided by this, we get 1. Then plus 1. Okay? So this is equal to 9 times... 8 squared is 64. And 8 squared is 64 here. Plus 1. Alright? Then plus 1. Alright? Now this is equal to... I hope I'm not too fast. So this is equal to 9 times... Remember that we don't have calculators. So let's simplify this even more as 60 plus 4. So we have this to be 60 plus 4. Alright? Multiplied by... Then this is 65. This is 65. Okay? Plus 1. Alright. Now we have this to be equal to 9 times... We have 60 plus 4. Into... This is 60 plus 5. Okay? Then plus 1. Now, let us try to solve this from here. From this side. Now, this can be expressed as 9 times... 60 times 60, right? 3600 Plus 60 multiplied by 5. 300 Plus 4 multiplied by 60. Plus 4 multiplied by plus 5. Plus 4 multiplied by 5. Then plus 1. Alright? Now 9 can be expressed... Okay, this is equal to 9 times... Now 60 times 60 is the same thing as 600 times 6. Which is 3600, right? So we have 3600. Yeah. 3600 I want to make sure. Okay. Yeah. That is it. 3600 Now, plus 60 times 5 is 300. Plus 4 times 6 is 240. Plus 4 times 5 is 20. Plus 1. Okay? Now this is equal to 9 times... Now let us add this together. So we have 3600. Plus 300. Plus 240. Plus...