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## Working with powers of 10

# Multiplying multiples of powers of 10

CCSS.Math:

## Video transcript

- [Voiceover] I would like
to multiply nine times 10 to the ninth power times negative two, times ten 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 nine
and the negative two first and then we can multiply
the 10 to the ninth and 10 to the negative third power. So if I were to change the order, we could write this as nine times, nine times, nine times negative two. Nine times negative two times 10 to the ninth power. Times ten, let me do it in that, in this color. Times ten to the ninth power. Times 10 to the negative third power. Times 10 to the negative third power. Now what's nine times negative two? Well, if nine times two is 18, nine times negative two
is gonna be negative 18. So that's negative 18. And what is 10 to the ninth
times 10 to the negative three? 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, time that same number
raised to another exponent, this is going to be the
same thing as that number, as that base, raised to
the sum of these exponents. This comes straight out of
our exponents properties. So this is going to be 10 to the, 10 to the nine plus negative three power. Nine plus, actually, let me
use those colors so you see where that nine and that
negative three came from. Nine plus negative three power. Nine plus, this color, I'm having
trouble changing colors. Nine plus negative three power. Now what's this gonna be? Well this is going to
be equal to negative 18 times times 10 to the, nine plus negative three, same thing as nine minus three, which is six. Negative 18 times 10 to the sixth power. And if you wanted to think about well what number is this? 10 to the sixth, that's
one with six zeros, this is a million. Negative 18 times a million, it's gonna be negative 18 million. Or we could say negative
18 times 10 the the sixth. 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.