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## 8th grade (Illustrative Mathematics)

### Course: 8th grade (Illustrative Mathematics) > Unit 7

Lesson 5: Lesson 12: Applications of arithmetic with powers of 10# 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.

## Want to join the conversation?

- what is 0^0 and why(6 votes)
- It is indeterminant because of a conflict of two properties:

1) anything to the 0 power is 1 (except 0)

2) 0 to any power is 0 (except 0)

So there is no way to pick which one should take priority(11 votes)

- What's 2 to the zeroth power?(0 votes)
- Two to the zero power will be 1. Any number to the zero power will be 1 (except zero). The exponent, or power, shows the number of times the base is being multiplied by itself. So if 2 were to be the base, and if zero was to be the exponent, then fundamental you are dividing 2 with itself.

2^1 is 2, and 2^2 is 4. Each time the exponent increase by 1, the base is multiplied by 2. By powering 2 by 0, you are thus decreasing the exponent by 1 (1-1=0) and dividing 2 by itself.(19 votes)

- Why was the final answer 18 NOT simplified to 1.8 given the exponential notation rule ?? this just confuses me(4 votes)
- Sal chose to write the result in standard form.

If he had written the answer in scientific notation, then it would have been: -1.8 x 10^7

Hope this helps.(7 votes)

- I was given the problem: 8*10^4 / 4*10^-5 = (APPRENTLY) 2*10^9

Sal went over what happens if u multiply a positive exponent by a negative exponent, but not if they were to be divided (in this video, at least.) What is the logic among dividing exponents?(1 vote)- When we divide a common base (the 10's in your example), you subtract the exponents.

Thus: 10^4/10^(-5) = 10^[4-(-5)] = 10^[4+5] = 10^9

Hope this helps.(9 votes)

- I'm Confused as well you see i have a learning disorder so its hard for me to focus on stuff like this so my question is how do you Multiply multiples of ten?(5 votes)
- wouldn't 10x10 be 100? why is it 10(4 votes)
- he was adding the exponents

when you have exponents that have the same base and they are being multiplied then you can add the exponents. example:

10 to the 4 power * 10 to the 5 power can be simplified to 10 to the 9th power

hope this helps!(3 votes)

- explain more. why add the exponents? sometimes we multiply. when do we add exponents and when do we multiply them? confusion. im very confused.(3 votes)
- Here are the properties:

Multiplying a common base, add exponents: a^n * a^m = a^(n+m)

A common base with one exponent raised to another, multiply exponents: (a^n)^m = a^(n*m)

If you get confused, write the problem out without using exponents. For example:

x^2 * x^3 = x*x * x*x*x

Rewrite in exponent form. The are 5 x's, so we get x^5. So, we basically added the original exponents.

(x^2)^3 = x^2 * x^2 * x^2 = x*x * x*x * x*x

Rewrite in exponent form. The are 6 x's, so we get x^6. So, we basically multiplied the original exponents.

Hope this helps.(4 votes)

- how do i multiply (9*10^9)(-2*10^-3)?(4 votes)
- First, you got to multiply 9 and -2. Then you multiply

(9) * (-2) * (10 ^ 9) * (10 ^ -3). You get (-18) * (10 ^ (9+(-3))). To get, -18*(10^6). to get, -18*1000000

= -18000000

If you like it drop an upvote pls.(0 votes)

- how old is too old(2 votes)
- when they cough up dust thx(2 votes)

- Why are we not using the FOIL method? Isn't this problem a binomial?(1 vote)
- No, a binomial has two terms which would require an addition or subtraction sign inside of each of the parentheses. They have multiplication signs instead.(4 votes)

## 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.