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### Course: Get ready for Algebra 1>Unit 5

Lesson 4: Exponent properties intro

# Exponent properties with quotients

Learn how to simplify expressions like (5^6)/(5^2). Also learn how 1/(a^b) is the same as a^-b. Towards the end of the video, we practice simplifying more complex expressions like (25 * x * y^6)/(20 * y^5 * x^2). Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• at why did sal have one in the numerator? we got nothing
• When we cancel out something completely and there's a blank, we put a 1 there.
• Why does `(ab^3)^3` not become `ab^9`? In the other videos Sal showed that `(a^x)^y = a^x*y`, so why does it not apply here?
• Yes, the rule you described does apply. However, the answer is not just ab^9 because the a is inside the parentheses and so the exponent of 3 outside the parentheses also applies to the a as well as to the b^3.
(In other words, there's another rule that also applies: (ab)^x = a^x b^x.)

Therefore, (ab^3)^3 = a^3 * (b^3)^3 = a^3 * b^(3*3) = a^3 b^9.

Have a blessed, wonderful day!
• The question is 42w^2 divided by 35w^4. Does that mean they both have the same bases?
• No - The exponents are on only the W's.
For the numbers, you would remove any common factor to reduce that portion of the fraction. For W's, you subtract the exponents.

Hope this helps.
• how do you do ((9^4)(7^5))^-11? Because there is no exponent that is the same in 9 and 7 to simplify to
• If you distribute the -11 to both of the equations, like so:
(9^4)^-11*(7^5)^-11
Then we multiply the exponents (because an exponent raised to a power is just multiplying the two together):
(9^-44)*(7^-55)
And then we put them in the denominator (because they have a negative exponent):
1/(9^44)(7^55)
(Which can then be simplified to something like... 3.41143722⋅10^−89)
• I understand none of this stuff☜(ﾟヮﾟ☜)😂😂😁
• Why is a number raised to a negative power the same as "1" divided by that same expression? I've been struggling to understand this fully for a while now, and any help would be greatly appreciated.
• So, you know that 3 to the first is 3, right? And 3 squared is 9, 3 cubed is 27, etc...
The pattern is that you divide by 3 when you go down, which makes sense, right?

Then 3 to the 0th is 1. So what is 3 to the negative first? It's simply 1/3. If this still doesn't make sense, then think of the fact that when you multiply, your exponent increases by an amount, and when you divide, your exponent decreases.

• My head is literally singing into the unknown math problem! But, I am a bit confused about .
• It's because of the communitive property, meaning the order of which you multiply doesn't matter, as long as you are only multiplying like terms. Hope this helps!
• What do we do if the denominator is different.