Destinyyyy
  • Destinyyyy
Cant remember how to solve this...
Mathematics
schrodinger
  • schrodinger
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Destinyyyy
  • Destinyyyy
Multiply. 5xy^5 / 3x^5y^3 * 6x^5y^6 / 25x^7y^10
Destinyyyy
  • Destinyyyy
-6x^5y^6 **
phi
  • phi
y^5 means y*y*y*y*y if you divide that by y^3 \[ \frac{y\cdot y\cdot y\cdot y\cdot y}{y\cdot y\cdot y} = y\cdot y \cdot \frac{ y\cdot y\cdot y}{y\cdot y\cdot y}= y\cdot y= y^2\] or the fast way: if you are dividing , subtract top exponent minus bottom exponent i.e. \[ \frac{y^5}{y^3}= y^2\] notice 5-3=2

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Destinyyyy
  • Destinyyyy
Okay thats ringing a bell...
Destinyyyy
  • Destinyyyy
but dont I need to simplify 25 and -6 into two smaller numbers?
phi
  • phi
is this the original problem: \[ \frac{5xy^5}{3x^5y^3} \cdot \frac{-6x^5y^6 }{25x^7y^{10}} \]
Destinyyyy
  • Destinyyyy
Yes
phi
  • phi
if so, we multiply top times top and bottom times bottom \[ \frac{5xy^5\cdot-6x^5y^6}{3x^5y^325x^7y^{10}} \] and you can reorder the top (and bottom) I would just start dividing the bottom into the top as much as possible
phi
  • phi
for example, I already figured out y^5/y^3 = y^2 so we can simplify to \[ \frac{5xy^5\cdot-6x^5y^6}{3x^5y^325x^7y^{10}} \\ \frac{5xy^2\cdot-6x^5y^6}{3x^5\cdot 25x^7y^{10}} \]
phi
  • phi
3 in the bottom can divide into -6 up top, to get -2 I would move the minus sign "out front". we get \[ -\frac{5xy^2\cdot2x^5y^6}{x^5 \cdot 25x^7y^{10}} \]
phi
  • phi
notice you have x^5 in the top and in the bottom. they "cancel out" (anything divided by itself is 1) so you have \[ -\frac{5xy^2\cdot2x^5y^6}{x^5 \cdot 25x^7y^{10}} = -\frac{5xy^2\cdot2y^6}{25x^7y^{10}}\]
phi
  • phi
notice you have 5 up top and 25 down below 25 is 5*5 so we have a 5/5 that cancel, and 5 remains down below.
Destinyyyy
  • Destinyyyy
Im trying to follow but im getting lost... I remember having to do the first step as --- 5*x*y^5/ 3*x^5*y^3 * 2*3*x^5*y^6/ 5*5*x^7*y^10
Destinyyyy
  • Destinyyyy
And then minus the exponents and all.
Destinyyyy
  • Destinyyyy
So I now have - 2/5
phi
  • phi
the way I do these (where everything up top is multiplied and everything down below is multiplied) is ignore everything except one thing up top and the same thing down below for example, if we look just at 5 up top and 25 below \[ \frac{5}{25} = \frac{5}{5\cdot 5} = \frac{1}{5} \] and I would replace the 5 up top by 1 and the 25 below with 5 and *everything else stays the same*
phi
  • phi
*** 5*x*y^5/ 3*x^5*y^3 * 2*3*x^5*y^6/ 5*5*x^7*y^10 *** yes that is good. (but is there supposed to be a minus sign in there) ?
Destinyyyy
  • Destinyyyy
Um okay?
Destinyyyy
  • Destinyyyy
Yes because of -6
phi
  • phi
ok. so if we just at the numbers we have \[- \frac{5\cdot 2 \cdot 3}{3 \cdot 5 \cdot 5 }\] one pair of 5's cancel, and so does the pair of 3's so yes we get \[ - \frac{2}{5} \]
phi
  • phi
now do the x's \[ \frac{x\cdot x^5}{x^5\cdot x^7} \] we could make the top x^6 and the bottom x^12 but I try to divide first. for example x^5 divided by x^5 cancels (i.e.=1)
phi
  • phi
is it clear how to simplify the x's or is it confusing?
Destinyyyy
  • Destinyyyy
So your talking about combining then but to try to divide first..
Destinyyyy
  • Destinyyyy
Do you mean subtract??
phi
  • phi
the rules might be confusing, but remember this: for example x^5 means x*x*x*x*x and if we divide by x^7 = x*x*x*x*x*x*x i.e. \[ \frac{x\cdot x\cdot x\cdot x\cdot x}{ x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}\]
Destinyyyy
  • Destinyyyy
I have this-- - 2y^2x^-2/ 5x^-4 y^-4
phi
  • phi
every time you have an "x" up top and "x" down below, they cancel out so just cancel them out in pairs.
Destinyyyy
  • Destinyyyy
Final answer- - 2/ 5x^6y^2
phi
  • phi
what do you get for \[ \frac{x\cdot x^5}{x^5\cdot x^7} \]?
phi
  • phi
I would try to keep the exponents positive (less confusing) \[ \frac{x\cdot \cancel{x^5}}{\cancel{x^5}\cdot x^7} = \frac{x}{ x^7}= \frac{1}{x^6}\]
Destinyyyy
  • Destinyyyy
Thank you for taking away 40 minutes of my time that I needed.
Destinyyyy
  • Destinyyyy
This question should of taken less then 5 minutes to solve.
Destinyyyy
  • Destinyyyy
Thank you for explaining things. But I did not need that. All I needed was a refresher. Im studying for my final exam.
phi
  • phi
oops \[ -\frac{2}{5} \frac{1}{x^6y^2}\]
Destinyyyy
  • Destinyyyy
I figured that out 6 minutes ago..

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