hello everybody this is Paul thank you for watching today's video tutorial today's lesson is going to be on exponents and roots now Before we jump right into exponents and roots I want to discuss something we all know a little bit about addition and subtraction now you'll find that the relationship between addition and subtraction is really the same as the relationship between exponents and roots so let's say you start with the number 4 and you add the number 3 to it you end up with the number 7 now what if we started with the number 7 and wanted to make our way back to the 4 while subtraction does the job for us 7 and then this time instead of adding 3 like we did over here we take away 3 and it brings us back to the 4 that we started with over here now multiplication and division also have the same relationship with one another say we have 5 times 2 and that gives us 10 and we want to start with the 10 and work our way back to 5 we simply divide instead of multiply and then the dividing by 2 brings us back to the 5 that we started with so now let's jump into exponents and roots let's start with the exponent 3 to the second power or 3 squared whichever you want to call it it's the same thing 3 squared or 3 to the second power now 3 is the base and the 2 is the exponent or the power and basically the power tells us how many times we're going to multiply the base by itself so this time we're going to do 3 multiplied by itself 2 times since we have an exponent of 2 3 times 3 is 9 so therefore 3 squared or 3 to the second power is simply 9 now what if we want to start at 9 and make our way back to 3 well the root does the job for us so the square root of 9 equals 3 now there's something missing here right here there's a number which we call the base and whenever the base is missing we just assume that that is the base 2 now the base tells us that base number 2 basically tells us that this is the power that this root undoes so this only works when it's the second root you can't take the third root of 9 and get back to 3 it has to be the second and the reason why is it's because we wish to the second power to get to 9 so therefore it has to be the second root which undoes it to get us back to 3 let's do 6 to the second power so this is the base 6 multiplied by itself 2 times 6 times 6 is 36 so 6 squared equals 36 now if we want to start with the 36 and make our way back to the 6 we just undo it by doing the square root of 36 now what if our power isn't two let's do 3 to the fourth power so this is the base 3 multiplied by itself 4 times 3 times 3 times 3 times 3 now 3 times 3 is 9 9 times 3 is 27 and 27 times 3 is 81 now starting at the 81 and working our way back to 3 we take route 81 but this time we're not dealing with the square root because the exponent was a 4 that brought us to the 81 so it has to be the 4th root in order to bring us back to the 3 so the 4th root of 81 brings us 3 because 3 to the 4th power bring eighty-one now the fourth root of 81 can also be written as 81 to the 1/4 power so if you want to write it in terms of the power you just put a fraction one divided by whatever the base of the root was let's try one more example two to the fifth power so this is the base two multiplied by itself five times 2 times 2 times 2 times 2 times 2 2 times 2 is 4 4 times 2 is 8 8 times 2 is 16 and 16 times 2 is 32 so now we start with the 32 and we want to work our way back to the 2 so we take route 32 and this time it's the 5th root because it took the 5th exponent to get us there so the 5th root of 32 undoes the process and brings us back to the 2 which can also be written as 32 to the 1/5 power writing the base in the denominator and there you go that's today's tutorial hopefully you've enjoyed this lesson if you've enjoyed my videos please subscribe I'll be putting out more videos in the near future and if there's anything specific you want to let me know I can make you a video about that topic and just leave me a comment and I'll see what I can do for you anyway as always have a great day and thank you for watching