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### Course: Pre-algebra>Unit 11

Lesson 5: 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
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!
• 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.
• 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.
• 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.
• Why is 10^x/10^y 10^z? Shouldnt ur be 1^z since 10/10 IS 1?
(1 vote)
• Remember, PEMDAS. The exponents must be done before the division. Since you don't know the values of the variables, the best you can do is apply the quotient rule of exponents which tell us that when we divide, we subtract exponents. And, the product rule that says when we multiply, we add exponents.
Assuming your problem is: (10^x/10^y) 10^z
= 10^(x-y)*10^z = 10^(x-y+z)

Hope this helps.
• 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.