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## College Algebra

### Course: College Algebra>Unit 7

Lesson 1: Exponent properties (integer exponents)

# Powers of products & quotients (integer exponents)

For any integers a and b and for any exponents n, (a⋅b)ⁿ=aⁿ⋅bⁿ and (a/b)ⁿ=aⁿ/bⁿ. These are worked examples for using these properties with integer exponents.

## Want to join the conversation?

• When doing this method,can the whole number be negative?Does it have a complete different name?
• Do you mean can the "base" of the exponent be negative?
Sure! The base is the number that you are applying the exponent to. The base can be positive, negative, fraction, decimal, etc.

(-3)^2 = 9
(-3)^(-2) = 1/(-3)^2 = 1/9
• Okay is it bad that I'm confused on what integers are?
• Integers are whole numbers that can be be negative or positive. (ex. -27, -2, 0, 3, 102)
• What is the point of converting the first problem to a fraction at ?, Sal said they were equivalent but seven to the 6th power dosen't add up to the same thing as three to the sixteenth, or am I missing something?
• If you are referring to when Sal changes `3^16 7^(-6)` into `3^16/7^6`, this is done to eliminate the negative exponent. When a problems is completely simplified, it would not have a negative exponent.

Hope this helps.
• Can someone help me at ?

I don't understand why Sal raised 4 to the 17th power, rather than the 14th power.

Anything helps!
• This is a known error in the video. Sal finds & corrects his error a little later in the video. If you are watching in regular mode (not full-screen mode), you would see a correction box pop up and tell you this was an error.
• Get me to 100 upvotes and I will donate \$100 dollars to khan academy.
• Did anyone's video start glitching out and putting these color-y square line glitches all over the video screen?!
• I still don't get the part of where you turn (2^2)^14 into 2^28. Can someone show me step by step?
• why was the video glitching out at -
• It's not glitching for me though. FYI it might just be your internet problems. :)
(1 vote)