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Hey everybody this is Paxton Smith again at real-time math comm your link to live online math help and in today's arithmetic series video I'm going to take a quick look at exponents just a little of help for everyone out there who's struggling with exponents make sure we understand that correct notation what it really means so here I've got up here 4 times 4 times 4 times 4 times 4 all right you can write this big long factored out thing as 4 to the fifth, so you can think of exponents really as repeated multiplication, so it's much easier to write 4 with a little superscript here 5 4 to the fifth power it's much easier to write that as you can tell then writing out this long list of factors here now with exponents you're always multiplying the base which is your big number here by itself a certain number of times and that number of times is indicated by the exponent or the power, and it's also a superscript so 4 to the fifth is again exactly the same as saying 4 times 4 times 4 times 4 times 4 ok, so another example is 4 squared or 4 cubed 4 squared is 4 to the second power 4 cubed is for the third and a common mistake is to think that 4 squared means to do 4 times 2 or the fourth to the fifth means to do 4 times 5 okay that's not what it means 4 squared means 4 times 4 which is 16 again I've given us here 2 to the 4th power and I just want to clarify that 2 to the 4th is written in exponential form now if you want to write it out, and it's factored form you can see 2 times 2 times 2 times 2 and the actual value 2 to the 4th when you do that 2 times 2 is 4 times 2 again is 8 times 2 one more time gives us 16 when you can from exponential form, and you write it just as a single number like we're used to seeing that's called standard form so just make sure you understand that standard form is just one number exponential form is going to be your base with the exponent again the number of times you're going to multiply that base by itself okay and lastly as an example I have here 5 times 5 times 5 times 7 times 7 in exponential form that would look like 5 cubed or 5 to the third power times 7 squared, so again this would be 5 cubed times 7 squared and in standard form we would go ahead and do 5 cubed, and we get 5 times 5 is 25 times 5 again and down here we get 125 from that and 7 squared is going to just be 7 times 7 and down here we get 49 so if you wanted to convert from this form here into standard form, and you go ahead and multiply 125 times 49 and now give you a total of 6,000 125 again that can also be written in exponential form as 5 cubed times 7 squared will keep coming back to more on exponents especially in the beginning algebra and intermediate algebra series, and we'll also look at some stuff with exponents coming up here soon in the arithmetic series when we look at fractions raised to an exponent so check out my website real time math com again I'm Paxton Smith, and thanks for tuning in have a great day
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