What is an Exponent? | An Intro to Exponents | Math with Mr. J

[Music] welcome to math with Mr J in this video I'm going to cover what is an exponent so this is going to be an intro to exponents and what they mean so let's jump right into our examples starting with number one where we have 5 to the^ of two now you'll notice that we have a larger number the five and then a smaller number in the corner the two the larger number is called the base so this right here the five this is our base now the two that's the exponent the exponent tells us how many times we need to multiply the base by itself so for number one our base of five needs to be expanded out so to speak and multiplied by itself to times so 5 to the^ 2 means 5 * 5 and that equals 25 so 5 to the^ of 2 equals 25 it means 5 * 5 a common mistake is thinking that this means 5 * 2 which equals 10 but now we know that this is not the case another important aspect of exponents I want to cover is how to say them for number one we can say 5 to the power of two we can also say 5 to the 2 power or an exponent of two actually has a special name we can say 5^ squared any number to the power of two we can say squared let's move on to number two where we have 5 to the power of three we can also say 5 to the 3 power or an exponent of three has a special name as well cubed so we can say 5 cubed knowing squared and Cubed is very important when it comes to exponents for this one we take our base of five and expand it out three times so 5 * 5 5 * 5 5 * 5 * 5 let's see what this equals well 5 * 5 that's 25 and then we have one more 5 so 25 * 5 equals 125 so 5 cubed equal 125 let's move on to number number three where we have 3 * 3 * 3 * 3 * 3 * 3 so it's currently in expanded form everything is expanded out let's write this in exponential form so as a base and an exponent our base is going to be the number that's expanded out the number being multiplied by itself so in this case our base is three our exponent is going to be how many times that number is expanded out how many times is that number being multiplied by itself well six so that's our exponent so we have 3 to the power of 6 or 3 to the 6 power let's see what this equals let's multiply everything here and there are multiple ways we can think through this and see what this seals I'm going to pair up all of our threes here so we have 3 * 3 3 * 3 and 3 * 3 we know that 3 * 3 is 9 so I'm going to start breaking this down and let's multiply 9 * 9 * 9 well 9 * 9 that's 81 and 81 * 9 that's going to give us a final answer of of 729 so 3 to the 6th power equals 729 and like I mentioned there are different ways to think through that and different paths you can take in order to get to that 729 for example you can just start multiplying threes as well so 3 * 3 is 9 then multiply that 9 by three and then that by three so on and so forth until you use all all 63s let's move on to number four where we have 9 sared so this means 9 * 9 9 * 9 equal 81 so 9^ 2ar = 81 let's move on to number five where we have 2 to the 5th power so this is 2 * 2 * 2 * 2 * 2 so let's start breaking this down and see what this equals 2 * 2 is four bring down all the twos we did not use so we have three other twos here 4 * 2 is 8 and we're left with two more twos 8 * 2 is 16 and then one more two so 16 * 2 that gives us an answer of 32 lastly number six we have 7 to the 4th power so this would be I'm going to come underneath here so I have enough room 7 * 7 * 7 * 7 so let's see what this equals well we know 7 * 7 is 49 so let's pair some sev's up here we have 49 over here as well so we can get to our final answer by doing 49 * 49 and that's going to give us a final answer of 2,41 so 7 to 4th power equals 2,41 so there you have it there's an intro to to exponents so what is an exponent and what does it mean I hope that helped thanks so much for watching until next time peace