Question

The expression 14^6 ÷ 14^4 is equal to _____.

14^2
2
14^10
1

Answer 1

i dont know how

Answer 2

?

Answer 3

\[\frac{a^6}{a^4}={a^6}{a^{-4}}=a^{6-4} =a^{2}\]

Answer 4

Would you like to work through it @Susan_Hester ?

Answer 5

yes please

Answer 6

ok so let's discuss what an exponent represents first.

Answer 7

So just like multiplication is shorthand for addition, exponents are shorthand for multiplication

Answer 8

does that make sense?

Answer 9

yeah

Answer 10

ok, so if we have \(2^3=2*2*2\) do you follow?

Answer 11

yes

Answer 12

ok so now, let's do a similar problem to yours: \[3^9 \div 3^6\]
Now first thing I am going to do here is write this as a fraction, I like them better.
\[\frac{3^9}{3^6}\]

Answer 13

so, if we wanted to do this the long but make sense way, we will expand 3^9 and 3^6 like so \[\frac{3*3*3*3*3*3*3*3*3}{3*3*3*3*3*3}\]

Answer 14

Do you understand to here?

Answer 15

yes

Answer 16

?
u there

Answer 17

so now, can you simplify the fraction?

Answer 18

yes?

Answer 19

9/6

Answer 20

it gets even simpler

Answer 21

3/2

Answer 22

how did you get 6 on the bottom?

Answer 23

i counted 6

Answer 24

ahhh, ok, no you can't do it that way, think about if you had \[\frac{12}{6}\] how would you simplify that?

Answer 25

2

Answer 26

12 divided by 6 is 2?

Answer 27

yea, so we are doing the same thing with all that multiplication

Answer 28

I could write 12/6 as \[\frac{3*2*2}{2*3}\]

Answer 29

need it in exponet form

Answer 30

I need to make 1/1 so because multiplication is commutative, I can pull the 3s, and 2s. (ie cancel them) \[\frac{\not3*\not 2*2}{\not 3*\not2}\] So I am left with only 2

Answer 31

now back to our exponent example, we use the same process, try one more time please \[\frac{3*3*3*3*3*3*3*3*3}{3*3*3*3*3*3}\]

Answer 32

14*14*\[14*14*14*14*14*14/14*14*14*14\]

Answer 33

can u just tell me the answer to my question please

Answer 34

ill give u a medal

Answer 35

?

Answer 36

You can do it just like the one above, or you can memorize the exponent rules found here. http://www.purplemath.com/modules/exponent.htm We were simply going to derive them so they make sense

Answer 37

never mind!