Question

i simplified (6x^9/4x^4) x (12x^2/3x^5) to 6/1 but i dont know what to do with the exponents. please help

Answer 1

\[(6x ^{9}/4x ^{4}) \times (12x ^{2}/3x ^{5})\]

Answer 2

6x^9/4x^4 = 6x^(5)/4 = 3x^(5)/2
12x^(2)/3x^(5) = 12/3x^(3) = 4/x^(3)
so

(3x^(5)/2) * (4/x^(3))
=
4(3x^(5))/x^(3)(2)
=
12x^(5)/2x^(3)
=
6x^(2)

Here are the steps remember that

x^(-1) = 1/x

so

6x^9/4x^4 = 6x^(9)x^(-4)
9-4 = 5 therefore 6x^(5)/4

Answer 3

the x^(-1) = 1/x is a very important rule that you will need to know for higher math :)

Answer 4

I made a mistake
6x^9/4x^4 = 6x^(9)x^(-4)/4

Answer 5

Do you understand?

Answer 6

Remember when multiplying exponents it is additive.
for example (1 + x)^(2) = (1+x)(1+x) its just an easier way to write it but if we went
(1 + x)^(2) * (1 + x)^(2) we would just have (1+x)(1+x)(1+x)(1+x) so it is an addditive process.

Now if we consider the rule that x^(-1) = 1/x

(1+x)/(1+x)
=
(1+x)^(1) * (1+x)^(-1)
=
(1+x)^(0) = 1

as anything to the power of 0 equals one
excluding 0^(0) which is indeterminate

Answer 7

Do you understand?

Answer 8

I hope that you read what I wrote because knowing this will really strengthen your skills with algebra

Answer 9

no i dont understand. all you did was confuse me

Answer 10

so understand that
(x) = (x)^(1) they are equivilent
same with
(x+1) = (x+1)^(1)
you can raise it to the power of one.

When mutilplying two like variables exponents are another way of showing how many times you are multiplying the same variable. So if we have x

x^(1) = x
but if we had
x^(2) = x * x
(x * x is the same as saying (x^(1) * x^(1)) so 1 + 1 = 2 thus x^(2)
do you understand so far?

Answer 11

Please stay with me as I'm doing this as a study break and I need to get back to work very soon, if you want me to explain this important concept to you

Answer 12

i am

Answer 13

x*x*x = x^(3)
same as saying
x^(1) * x^(1) * x^(1) = x^(3)
1 + 1 + 1 = 3

Answer 14

yeah i know that concept. but what do i do with my exponents to simplify them?

Answer 15

Ok there is a rule

x^(-1) = 1/x

Answer 16

remember this rule

Answer 17

so taking in account that rule

x^(1)/x^(1) = x^(1) * x^(-1) = x^(0) = 1
1 + (-1) = 0
remembering that + * - = -
Also remember that anything to the power of 0 is equal to 1 (excluding 0 which you can't raise to the power of 0)

5^(0) = 1
y^(0) = 1
etc

Answer 18

so to

6x^(6)/4x^(4)
=
(6x^(6) * 4x^(-4))/4 = 6x^(2)/4
6 + (-4) = 6 - 4 = 2

Answer 19

12x^(2)/3x^(5)
=
12x^(2)x^(-5)/3 = 12x^(-3)/3 = (12/3)(1/x^(3)) = 12(1)/3x^(3) = 12/3x^(3)
2 + (-5) = 2 - 5 = -3

x^(-3) = 1/x^(3)

Answer 20

I hope this helps and you are just not even more confused it is some what logical if you jsut accept the rule that

x^(-y) = 1/x^(y)

y being any number

Answer 21

If you are still lost tell me what you are not getting and I will try to explain it better. Which will be kind of hard because there is only so many ways to explain a concept

Answer 22

Also remember that this can be only done with like variables or constants (like 2)
2/2 = 2^(1)/2^(1) = 2^(1)2^(-1) = 2^(0) = 1
1 + (-1) = 1 - 1 = 0

Answer 23

also remember that larger numbers can represent smaller numbers
8/2
=
2/2*2 = 2^(3) = 8
=
2^(3)/2^(1)
=
2^(3) * 2^(-1) = 2^(2) = 4
3 + (-1) = 3 - 1 = 2

Answer 24

this sort of explains division I find

Answer 25

sorry
2*2*2 = 2^(3) = 8

but yeah I will wait for you to respond.

Answer 26

Or you can just give up and take the answer, and I can just accept I wasted my time lol

Answer 27

no you didnt lol. i figured it out

Answer 28

Great :)