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### Course: 8th grade>Unit 1

Lesson 9: Working 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
• 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
• 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.
• What's 2 to the zeroth power?
• 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 sceintific notation
• For example, here are standard numbers in scientific notation:
500 = 5 x 10²
5,500,000,000 = 5.5 x 10⁹
0.000000055 = 5.5 x 10⁻⁹
• wouldn't 10x10 be 100? why is it 10
• 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!
• explain more. why add the exponents? sometimes we multiply. when do we add exponents and when do we multiply them? confusion. im very confused.
• 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.
• 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?
• let me give you an example 10^2x10^3 is 10x10 x 10x10x10 which would equal 100x1000=100,000 or 10^5 if you notice it's all about moving the comma to the right or left. Hope this helps Good Luck :)
• 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?
• 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.
• His voice is too low, I can't hear a thing. I have to put the volume to 100% so I can hear him properly.