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### Course: Pre-algebra>Unit 11

Lesson 4: Exponent properties (integer exponents)

# Multiplying & dividing powers (integer exponents)

For any base a and any integer exponents n and m, aⁿ⋅aᵐ=aⁿ⁺ᵐ. For any nonzero base, aⁿ/aᵐ=aⁿ⁻ᵐ. These are worked examples for using these properties with integer exponents.

## Want to join the conversation?

• in how did he get 1/4 3
• When you have a negative power, you are taking the reciprocal of the number, and keep the power. So 2^(-2)=1/2^2. So 4^(-3)=1/4^3
• How do you divide exponents by exponents? I kinda really don't understand that part.
• An easier way to think about this is to treat the multiplication sign as an addition sign and treat the division sign as a subtraction sign. I'll put an example down below! :)
Therefore, 4_^-3 x 4_^5 is equal to 4_^2.
You would add -3 + 5, which is equal to 2. Then keep the 4 and put the 2 as the exponent!
• If negative exponents such as 10^-5 is equal to 1/10^5, what would fractions with negative exponents such as 1/10^-5 be equal to?
• Apply the same rule you have cited. As you put it (10)^-5 = 1/(10)^5
The expression in question is 1/(10)^-5.
Lets see! We can write (10)^-5 as 1/(10)^5 (as you wrote).
So 1/(10)^-5 can essentially be written as 1/(1/10^5)
Which is nothing but 10^5 itself( We're basically taking the reciprocal of 1/10^5)

So 1/(10)^-5 =10^5
Cheers!

EDIT: Since perhaps that's a bit long, you can remember it for a general case as:
1/a^-m = a^m
where a and m can be any of positive or negative integers(but not zero!)
Hope that helps!
• Why does this exist
• so that its easier to write repeated multiplication without it being really lomg
• how do you do it when both powers are negative and you are multiplying.
• when both powers are negative, and you are multiplying,the negatives cancel eachother out so you would get a positive power.
• my comment will go down in history
• Yes it will bentley.dever, yes it will.
• Make no sense
• For the dividing part, how did you make the exponent of 12^-5 positive and the exponent of x^5 negative?