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## Pre-algebra

### Unit 11: Lesson 5

Working with powers of 10

# Multiplying multiples of powers of 10

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.
• what is 0^0 and why
• 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
• 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?
• 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.
• Why was the final answer 18 NOT simplified to 1.8 given the exponential notation rule ?? this just confuses me
• 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.
• 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?
• 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?
• 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.
• 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
• 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.