Question

*MEDAL AND FAN*

Find the common factor of the monomials.

a^2b^3, ab^3

Answer 1

Important thing to remember on these is your property of exponentials a ^ x ( a ^y) = a^x+y

Answer 2

Huh? Sorry, I'm not quite understanding what you're saying.

Answer 3

Both terms have a common base numerical exponent with respect to the properties

Answer 4

Yes.

Answer 5

If you have a to some power x and you multiply by another factor a to some other power call it y , the product will still have base a and the exponent will be x+y

Answer 6

So a is factor of both judging from the bases but both terms also have a numerical factor in there exponents

Answer 7

What could you factor out of both terms know that multiplying the factors in the end will end up with a submation of the exponential parts?

Answer 8

I'm sorry, I meant to say greatest common factor.

Answer 9

I thought that's what you meant..

Answer 10

My question for you is still relevant

Answer 11

I hate to admit this, but the words you're using are too big.

Answer 12

What class is this for?

Answer 13

Pre-Algebra.

Answer 14

And what's your age may I ask?

Answer 15

14.

Answer 16

okay, there's a rule in pre-algebra

when you have a number like 2 for instance and it is raised to the 3rd power that means 2 times 2 times 2 right which is?

Answer 17

8

Answer 18

So 2^3 = 8

Now the rule deals with exponents, here we have the exponent of 3

Answer 19

what if we have (2^6)(2^15) though, who really wants to multiply 2 that many times ? Well the rule says there's a short cut

Answer 20

And what would that be?

Answer 21

I can say (2^3) times (2^15) is equal to 2^18

Answer 22

Uh huh but wouldn't that be more difficult?

Answer 23

no, both ways are equivalent so either way can represent our number

Answer 24

2^3 and 2^15 can be said to be factors of 2^18

Answer 25

Uh huh.

Answer 26

In fact, 2^(any number from 0 to 18) can be said to be a factor of 2^18

Answer 27

Huh, not 5?

Answer 28

Because any number between 0 to 18 will add up to 18 given another factor

Answer 29

2^5 is a factor of 2^18 because there's 2^13, make sense?

Answer 30

Yes.

Answer 31

So if we had numbers c and d as exponents with base 2 what would we have as a product?

Answer 32

We'd have 2^(c+d)

Answer 33

Do you think you understand the rule now?

Answer 34

http://www.sosmath.com/algebra/logs/log3/log3.html

Answer 35

These rules may come in handy

Answer 36

But for this problem we only need focus on rule 1.

Answer 37

Do you follow?

Answer 38

Yes.

Answer 39

the common factors for this is ab^2(ab)