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# Multiplying multiples of powers of 10

## Video transcript

I would like to multiply 9 times 10 to the 9th power times negative 2 times 10 to the negative third power and so I encourage you pause the video see if you can work through this alright so the first thing I would want to do is let's just change the order of multiplication let's multiply the 9 and the negative 2 first and then we can multiply the 10 to the 9th and 10 to the negative third power so if I were to change the order we could write this as 9 times 9 times 9 times negative 2 9 times negative 2 times 10 to the ninth power times 10 let me do this color times 10 to the 9th power times 10 to the negative third power times 10 to the negative third power now what's 9 times negative 2 well 9 times 2 is 18 9 times negative 2 is going to be negative 18 so that's negative 18 and what is 10 to the 9th times 10 to the negative 3 well if I have a number raised to some exponent times that same number I have 10 I have the same base for both of these times that same number raised to another exponent this is going to be the same thing as that number as that base raised to the some of these exponents this comes straight out of our exponent properties so this is going to be 10 to the 10 to the 9 plus negative 3 power 9 plus actually let me use those colors so you see where that 9 and the negative 3 came from 9 plus negative 3 power 9 Plus this color I'm having trouble changing colors 9 plus negative 3 power now what's this going to be well this is going to be equal to negative 18 x times 10 to the 9 plus negative 3 same thing as 9 minus 3 which is 6 negative 18 times 10 to the 6th power and if you wanted to think about what what number is this 10 to the 6 that's one with six zeros this is a million negative 18 times a million it's going to be negative 18 million or we could say negative we could say negative 18 times 10 to the 6 either way but this is another way we could have written this we could have written this as negative 18 negative 18 let me write the zeros with the green just for fun negative 18 negative 18 million either way is a legitimate way to represent this number