baby456
  • baby456
(3x^2 y)^3/(6x^-2 y^5) please help medal + fan and please explain it.
Mathematics
schrodinger
  • schrodinger
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hlambach
  • hlambach
Your missing a part there after 6x
hlambach
  • hlambach
oops *You're haha
baby456
  • baby456
-2

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baby456
  • baby456
is right there
hlambach
  • hlambach
What power is 6x being raised to? 2y^5?
baby456
  • baby456
-2
baby456
  • baby456
let me draw it
hlambach
  • hlambach
Okay.
baby456
  • baby456
|dw:1435273567323:dw|
hlambach
  • hlambach
Got it. :) So you're simplifying it, right?
baby456
  • baby456
yes
anonymous
  • anonymous
use your basic properties of exponents. \(\dfrac{a^M}{a^N}=a^{(M-N)}\\\) etc.
baby456
  • baby456
ok
baby456
  • baby456
|dw:1435273964905:dw|
hlambach
  • hlambach
Tip: First simplify \[(3x ^{3}y)^{3}\]
baby456
  • baby456
9x^9y^3
hlambach
  • hlambach
Good, now you can use the formulas Jenny gave you.
hlambach
  • hlambach
Hold on, 3^3 is what?
baby456
  • baby456
|dw:1435274627143:dw|
anonymous
  • anonymous
3^3=3*3*3 3^3=/=3*3
hlambach
  • hlambach
Again, what Jenny said... I was wrong to say that you were right in your simplification.
baby456
  • baby456
oh i simpfieed it 27X^6y^3
baby456
  • baby456
|dw:1435274935189:dw|
hlambach
  • hlambach
There you go.
baby456
  • baby456
ok so how about the bottom
hlambach
  • hlambach
Well, now all you have to use is the Exponent Rule: \[\frac{ x ^{a} }{ x ^{b} } = x ^{a-b}\]
baby456
  • baby456
how about the 6
baby456
  • baby456
do you subtract 27-6
hlambach
  • hlambach
Well, this is kind of hard to explain in text, but I'll try. :) You have (ignoring the y) 27x^9 ------ 6x^-2 To divide it into 27, make it 2(3x^-2) since 3 can be divided into 27. Then use the exponent rule.
baby456
  • baby456
how? again
baby456
  • baby456
|dw:1435275710920:dw|
hlambach
  • hlambach
|dw:1435275705062:dw| SOrry for my terrible drawing skills haha. Now just divide out the 3x^-2
baby456
  • baby456
|dw:1435275773927:dw|
baby456
  • baby456
how
hlambach
  • hlambach
Just divide 27x^9 ------ 3x^-2 You will leave the 2 at the bottom.
baby456
  • baby456
9x^7
hlambach
  • hlambach
remember its x^a --- = x^a - b x^b
hlambach
  • hlambach
9 - (-2) is what?
baby456
  • baby456
x to 6 not x to the 9
anonymous
  • anonymous
split it up like this \(\dfrac{(3x^2 y)^3}{(6x^{-2} y^5) }=\dfrac{27x^6y^3}{6x^{-2}y^5}=\dfrac{27}{6}*\dfrac{x^6y^3}{x^{-2}y^5}\)
baby456
  • baby456
i am so confused
anonymous
  • anonymous
read your textbook. she's explained the property several times over
baby456
  • baby456
i dont have a textbook
baby456
  • baby456
still confused @jenny1994 is confusing me
hlambach
  • hlambach
Let's go with Jenny's way For now, focus on simplifying x^6 y^3 ------- x^-2y^5
hlambach
  • hlambach
Using the rule that I am too lazy to write out. (Just look above)
anonymous
  • anonymous
you can't follow a simple pattern? \(\large \dfrac{x^a}{x^b}=a^{(a-b)}\implies \dfrac{x^6}{x^{-2}}=?\)
anonymous
  • anonymous
x^(a-b)*
hlambach
  • hlambach
We can do this Jenny... haha Patience is a virtue. I wish I could put "OpenStudy Math Tutor on my transcript.
anonymous
  • anonymous
Don't mention openstudy, but say you tutor. Resumes are all about embellishment
hlambach
  • hlambach
Ha, I was joking, but that's a good idea!
hlambach
  • hlambach
Sorry, back on subject.
baby456
  • baby456
who way should i follow
hlambach
  • hlambach
Go with Jenny's Simplify x^6 y^3 ------- x^-2 y^5
baby456
  • baby456
you lost me at what to do about the bottom part please explain more
hlambach
  • hlambach
Using the rule that has been mentioned several times, thus I won't write it out again, simplify. EXAMPLE x^4 --- = x^(4-2) = x^2 x^2 Get it? But to that do your formula
hlambach
  • hlambach
*but do that to your formula.
baby456
  • baby456
so is it x4 since its 6-2
hlambach
  • hlambach
I'm sorry, I typed it wrong, it's x^9 y^3 ------ x^-2 y^5 So it would be x^11 (since 9 - (-2) = 11) But you grasped the concept. Now what about the y?
baby456
  • baby456
where are you getting x^9 from
hlambach
  • hlambach
From when you simplified (3x^3 y)^3 = 27x^9 y^3
baby456
  • baby456
(3x^2 y)^3= 27X^6y^3
baby456
  • baby456
2^3=6
zepdrix
  • zepdrix
Baby the subtraction comes from the rule, the bottom number also had a negative so don't let that extra negative get lost in the process! :)\[\Large\rm \frac{x^{\color{orangered}{6}}}{x^{\color{royalblue}{-2}}}=x^{\color{orangered}{6}-\color{royalblue}{-2}}\]You don't get x^4, see that?
zepdrix
  • zepdrix
2^3 does not equal 6. I think you meant 2*3 = 6 :)
hlambach
  • hlambach
Oh, I'm sorry. But remember cubed mean 2 * 2 *2
baby456
  • baby456
OPPS SORRY
baby456
  • baby456
SO THEN X=8
hlambach
  • hlambach
Hey, I gotta run. @zepdrix could you take over?
zepdrix
  • zepdrix
you mean for the final power on x? for the 6 - - 2? ya that looks better baby :)
zepdrix
  • zepdrix
ya you get outta here missy :P hehe
hlambach
  • hlambach
haha, thanks, I;m already running late. :)
zepdrix
  • zepdrix
So you understood this first step, yes?\[\Large\rm \frac{(3x^2 y)^3}{6x^{-2} y^5}=\frac{27x^6 y^3}{6x^{-2} y^5}\]And then did you understand the part with the x's?\[\Large\rm \frac{27\color{orangered}{x^6} y^3}{6\color{orangered}{x^{-2}} y^5}=\frac{27\color{orangered}{x^8}y^3}{6y^5}\] I'm just trying to figure out where we're at :O This thread is so long and messy
baby456
  • baby456
YEP
zepdrix
  • zepdrix
\[\Large\rm \frac{27x^8\color{royalblue}{y^3}}{6\color{royalblue}{y^5}}=\frac{27x^8\color{royalblue}{y^?}}{6}\]What about the y's? :) What do you think will happen there?
baby456
  • baby456
3-5=-2
zepdrix
  • zepdrix
\[\Large\rm \frac{27x^8\color{royalblue}{y^{-2}}}{6}\]Mmmm good. As a final step, you want to notice that the 27 and 6 share some factor.
baby456
  • baby456
3
zepdrix
  • zepdrix
\[\Large\rm \frac{27x^8y^{-2}}{6}=\frac{9\cdot3x^8y^{-2}}{2\cdot3}\]Yah that sounds right
zepdrix
  • zepdrix
\[\Large\rm \frac{9\cdot\cancel3x^8y^{-2}}{2\cdot\cancel3}\]
zepdrix
  • zepdrix
Sometimes your teacher will ask for the final answer with NO NEGATIVE POWERS. Do you understand how to deal with the y if you have to get rid of the negative power? :o
baby456
  • baby456
NOPE
zepdrix
  • zepdrix
mm k, well our exponent rule tells us to flip it. if its in the numerator, it gets tossed down the denominator and the sign changes on the power. if it's in the denominator it goes up to the numerator and the sign changes on the power. examples:\[\Large\rm \frac{1}{2x^{-7}}=\frac{x^7}{2}\] \[\Large\rm \frac{x^{-4}}{3}=\frac{1}{3x^4}\]
baby456
  • baby456
OH I REMEMBER THIS YOU JUST SWITCH IT LIKE A RECIPROCAL
zepdrix
  • zepdrix
good good :) reciprocal, and change from negative to positive
baby456
  • baby456
OK THANKS I HAVE TO GO NOW
baby456
  • baby456
THANKS FOR ALL YOUR HELP
baby456
  • baby456
sorry about caplocks
zepdrix
  • zepdrix
\[\Large\rm \frac{9x^8y^{-2}}{2}=\frac{9x^8}{2y^{2}}\]so ya that will fix the y :)
zepdrix
  • zepdrix
np

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