If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Course: Integrated math 1>Unit 13

Lesson 1: Exponent properties review

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?

• 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)
• 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
• 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.
• 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?
• Since there are two exponents(one inside the parentheses and one outside), you multiply the exponents together to make one. in this case there is a ^2 and ^14, so you multiply 2 and 14 to get 2^28
(1 vote)
• why was the video glitching out at -
• It's not glitching for me though. FYI it might just be your internet problems. :)
• wy don't you multiply the 3 and the 7 by the -2 power
• You never multiply the base of an exponent with the exponent. Exponents represent shorthand for repetitive multiplication of the base value. They tell you how many of the base you need to multiply together. The properties of exponents, tell us:
1) To multiply a common base, we add their exponents
2) To divide a common base, we subtract their exponents
3) When one exponent is raised to another, we multiply exponents.
4) When multiply factors are in parentheses with an exponent outside, we apply the exponent to all factors inside by multiplying the outer exponent with each factor's exponent.

The last two properties are being shown in the video.
[3^(-8) * 7^3]^(-2)
Apply the exponent -2 to each exponent inside the parentheses by multiplying them. You get:
3^16 * 7^(-6)

Hope this helps.