[Music] welcome to math with mr j [Music] 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 five to the power 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 2 times so 5 to the power of 2 means 5 times 5 and that equals 25 so 5 to the power of 2 equals 25 it means 5 times 5. a common mistake is thinking that this means 5 times 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 1 we can say 5 to the power of 2 we can also say 5 to the second power or an exponent of 2 actually has a special name we can say 5 squared any number to the power of 2 we can say squared let's move on to number 2 where we have 5 to the power of 3 we can also say 5 to the third power or an exponent of 3 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 5 and expand it out 3 times so 5 times 5 times 5. 5 times 5 times five let's see what this equals well five times five that's 25 and then we have one more five so 25 times five equals one hundred twenty-five so five cubed equals one hundred twenty-five let's move on to number three where we have three times three times three times three times three times three 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 sixth 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 equals i'm going to pair up all of our threes here so we have three times three three times three and three times three we know that three times three is nine so i'm going to start breaking this down and let's multiply 9 times 9 times 9 well 9 times 9 that's 81 and 81 times 9 that's going to give us a final answer 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 three times three is nine then multiply that nine by three and then that by three so on and so forth until you use all six threes let's move on to number four where we have nine squared so this means nine times nine nine times nine equals eighty-one so nine squared equals eighty-one let's move on to number five where we have two to the fifth power so this is 2 times 2 times 2 times 2 times 2. so let's start breaking this down and see what this equals 2 times two is four bring down all the twos we did not use so we have three other twos here four times two is eight and we're left with two more twos eight times two is sixteen and then one more two so sixteen times two that gives us an answer of thirty two lastly number six we have seven to the fourth power so this would be i'm going to come underneath here so i have enough room seven times seven times 7 times 7 so let's see what this equals well we know 7 times 7 is 49 so let's pair some sevens up here we have 49 over here as well so we can get to our final answer by doing 49 times 49 and that's going to give us a final answer of four 2400 one so seven to the fourth power equals two thousand four hundred one so there you have it there's an intro 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 you