Advanced Distributive property?

[EddieG]

My class was assigned 5 problems pertaining to the distributive property combined with a section dubbed "Algebra and Exponents" I have looked at the rules and didn't see anything against it, so I will post the questions and my Associated work.

#1 (8x^3y^-4z^17)^2 (12xy^3z)^3
(64x^-6y^-8z^34) (1728x^3y^9z^3)
Final Answer= 110,592x^3yz^37

Going to just post one at a time as they are looked over.

Right? Wrong?

 

[Loren]

(8x^3y^-4z^17)^2 (12xy^3z)^3

If your problem is \(\displaystyle (8x^3y^{-4}z^{17})^2(12xy^3z)^3\) then I disagree with your answer regarding the exponent for x.

 

[EddieG]

Hmm...not following that one? *edit* What do you think X should be?

 

[mmm4444bot]

… not following that one? … What do you think [the exponent on x] should be?

Hi Eddie:

With respect to the variable x only, you typed the exercise as (x^3)^2 * (x)^3.

This equals x^6 * x^3, but your work shows x^(-6) * x^3.

It looks like you made a typographical error on either your post of the original exercise or on your work.

As you typed it, the correct answer is x^9 because 6 + 3 = 9.

If there is a negative sign missing somewhere on the original exercise, then it's possible that the correct answer is supposed to be x^3.

Please proofread your typing. If you still cannot find your error, then let us know.

 

[EddieG]

8x^-3y^-4z^17)^2 (12xy^3z)^3 This is the correct typing, so I did forget a negative on the first X value.

 

[mmm4444bot]

(8x^-3y^-4z^17)^2 (12xy^3z)^3 This is the correct typing, so I did forget a negative on the first X value.

Okay. That's a different error than what I thought you might have done.

So, with respect to the variable x only, we have the following.

[x^(-3)]^2 * (x)^3 = x^(-6) * x^3 = x^(-6 + 3) = x^(-3)

-

Final Answer = 110592 x^3 y z^37

Did you forget to type the negative sign on your answer, too?

 

[EddieG]

ugh...i hate it when i do dumb stuff like that.. heres problem number two... sorry i dont know how to do the fancy forumula style, this might be a little rough..

#2. (-12x^-3y^-4z^3)
(2x^4y^3z^10)

This One i thought was fairly simple and ended up with....
-6
x^2 y^7 z^7

 

[mmm4444bot]

… i dont know how to do the fancy forumula style …

You don't need fancy typing; use grouping symbols to clearly show mathematical expressions. (There's a drop-down menu at the top of the page titled, "Forum Help". Point to it, and then select "Karl's Notes - Typing Math" for more information.)

[ -12 x^(-3) y^(-4) z^3 ] / [ 2 x^4 y^3 z^10 ]

-

-6
x^2 y^7 z^7

Check your arithmetic on the exponent for x.

The rest is correct.

 

[EddieG]

Last ones

#3. (4y^9z^15)^3 (-32xyz^4)
(-24z^14)^2 * (16x^5y^13z^-12)

3z^2 <--- Answer
x^4y^3


#4. (-16x^7y^12)^5
Answer= -80x^35y^60



#5. (4x^(-5)z^10) / (2x^3y^4) To the left of the signs is a fraction as is the right side so rather than the
(-2x^5y^4z^2) / (16y^12z^3) numerators diveded and the denominators, it should be the first half by the
second half.
-16y^4z^11 <-- Answer
x^3




Thanks ahead of time to anyone who may check over this by morning.

 

[Denis]

#3: way off! I get (-2 y^15 z^33) / (9 x^4) ; NO, I ain't typing out the steps :shock:

#4: close; your "60" should be 16^5 (not 16 * 5)

#5: you show:
(4x^(-5)z^10) / (2x^3y^4)
---------------------------------
(-2x^5y^4z^2) / (16y^12z^3)

which is (see NOTE):
[(4 x^(-5) z^10) / (2 x^3 y^4)] * [(16 y^12 z^3) / (-2 x^5 y^4 z^2)]

and that simplifies to -(16 y^4 z^11) / x^13

NOTE: (a / b) / (c / d) = (a / b) * (d / c)

 

[EddieG]

"#4: close; your "60" should be 16^5 (not 16 * 5)"

I don't think i'm following you there. (x^7)^5 = X^35....right? Then by the same method (y^12)^5 should equal y^60.

 

[Denis]

I'm NOT talking about the "y" (that's ok); I'm talking about the "16" :shock:

> (-16x^7y^12)^5
> Answer= -80x^35y^60

16^5 <> 80

 

[EddieG]

Realized it when I got to class and was checkin it with a friend, thanks for everything!