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Multiplying multiples of powers of 10

Let's multiply (9 * 10^9) (-2 * 10^-3) using the power of exponents! Change the order of multiplication to make it easier, multiply the non-powers first. and then simplify the powers of 10. Remember, multiplying by a negative changes the sign of the product. It's all about using exponent properties to simplify the product.

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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.