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: Math (NSDC) - English>Unit 7

Lesson 1: Properties of exponents

# Worked example: Exponent properties

Use exponent properties to simplify a challenging expression. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Would the answer still be correct if it is written as 5a^7*b^-1 rather than the fraction form?
• Yes that would be correct too.
But completely simplified would be in fraction form.
• with the end result, 5a to the power of 7 over b, could you still put it as 5b over a to the power of 7? if not, why does a to the power of 7 have to be over b?
• The positive exponents go in the numerator and the negative exponents go in the denominator. That is why 5 is on top with a^7 and b is on the bottom. If you wanted to move b to the numerator along with 5a^7, you would have to write it as b^-1, to indicate it is a negative exponent, as Sal did. Otherwise, if you write it as b and leave it in the numerator , people will assume it's a positive exponent,as positive exponents go in the numerator. 5b/a^7 would mean b is a positive exponent (which it is not) and a^7 is a negative exponent, which it is not. Putting 5 in the numerator, however, would be acceptable, but putting b in the numerator is not (unless written with a negative exponent of 1).
• When I type this 6/5y^2 the answer shows 6/5 with the y^2 not being in the denominator and instead being on the right of the whole 6/5. How do I type it to where it goes in the denominator?
• Type: `6 / (5y^2)`
It is very important to use parentheses when typing these expressions, to make sure the software knows what you mean. There is no harm in adding extra parentheses just to be sure.
• Like what Sal did in with the a^9/a^2 turned into a 9^7. So if I had a b^4/b^2 then i would come out with a b^2. right?
• When the is 5a to the 7th power over b, and b was to the negative 1st power, does that mean that the number with the negative exponent goes on the bottom of the fraction when simplified?
• Is this the problem you mean?
5a^7 / b^-1
The b^-1 in the denominator can be changed to b^1 in the numerator.
THen you have:
5a^7b^1

If you have a negative power in the numerator, it becomes positive in the denominator. If you have a negative power in the denominator, it becomes positive in the numerator.
• At I notice that the final product of the equation is 5a^7/b but could we put a 1 after 5a^7 so that it looks like 5a^7 1/b? I am a bit confused so please forgive me if what I write doesn't add up to what is actually in the seminar. and if this is possible, can I then add a + symbol so that it looks like 5a^7+1 over b??

Thanks in advance for the help!
• you are correct that 5a^7/b is the same as (5a^7)1/b. But No, you can not use a plus sign. It would be 5 times (a^7) times (1/b). or 5*(a^7)*(1/b).

I hope that helps.
• So if you can flip a part of a denominator with a negative exponent, what do you flip? just exponent? Base? Coefficents?
• 24^3= 13824
Because if you do 24 times 24 times 24 you get 13824
(1 vote)
• When the is 5a to the 7th power over b, and b was to the negative 1st power, does that mean that the number with the negative exponent goes on the bottom of the fraction when simplified?