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## Pre-algebra

# Multiplying multiples of powers of 10

CCSS.Math:

Learn how to multiply (9 * 10^9) (-2 * 10^-3).

## Want to join the conversation?

- What's 2 to the zeroth power?(1 vote)
- 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.(14 votes)

- what is 0^0 and why(4 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(6 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?(4 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.(7 votes)

- Why was the final answer 18 NOT simplified to 1.8 given the exponential notation rule ?? this just confuses me(2 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.(2 votes)

- Why does order of operations does not apply with powers of 10? According to PEMDAS, shouldn't we first solve the problem inside the parentheses, and the exponents, rather than removing 9 and -2 from their place and multiplying them first?(2 votes)
- The problem has 4 items that are being multiplied.

The associative property of multiplication and the commutative property of multiplication lets use regroup and move the numbers around.

For example: 2(3*5) can be changed to (2*3)*5 or to (2*5)*3. All of them equal 30.

Hope this helps.(1 vote)

- So taking a negative power is the same as just adding zeros in front of the number. For example, 10^-4 is 0.0001. Right?(0 votes)
- Yes it is the same as adding zeros in front of the number. But when you get other numbers like 98 or 76 etc. you'll add the zeros in front of the number and in the "10"'s place will be taken up by the number that you are given.

Hope it helps!!

P.S- If you post a question under a video or article, will you be able to see your questions on the question page?? Please up vote if yes.(4 votes)

- Would we be able to do something like 5 to the power 10 plus 5 to the power 10 to equal 10 to the power 10?(1 vote)
- No you could not do that, it would be 2*5^10 where your statement would read (2*5)^10 = 2^10*5^10(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.(2 votes)

- what if you have instead of having 10 to the 9th power and 10 to the -3th power, you have 10 to the 7th power on both numbers?(1 vote)
- When multiplying values with a common base, add their exponents.

10^7 * 10^7 = 10^(7+7) = 10^14

Hope this helps.(2 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.