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Destinyyyy

  • one year ago

Cant remember how to solve this...

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  1. Destinyyyy
    • one year ago
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    Multiply. 5xy^5 / 3x^5y^3 * 6x^5y^6 / 25x^7y^10

  2. Destinyyyy
    • one year ago
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    -6x^5y^6 **

  3. phi
    • one year ago
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    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

  4. Destinyyyy
    • one year ago
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    Okay thats ringing a bell...

  5. Destinyyyy
    • one year ago
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    but dont I need to simplify 25 and -6 into two smaller numbers?

  6. phi
    • one year ago
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    is this the original problem: \[ \frac{5xy^5}{3x^5y^3} \cdot \frac{-6x^5y^6 }{25x^7y^{10}} \]

  7. Destinyyyy
    • one year ago
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    Yes

  8. phi
    • one year ago
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    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

  9. phi
    • one year ago
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    for example, I already figured out y^5/y^3 = y^2 so we can simplify to \[ \frac{5xy^5\cdot-6x^5y^6}{3x^5y^325x^7y^{10}} \\ \frac{5xy^2\cdot-6x^5y^6}{3x^5\cdot 25x^7y^{10}} \]

  10. phi
    • one year ago
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    3 in the bottom can divide into -6 up top, to get -2 I would move the minus sign "out front". we get \[ -\frac{5xy^2\cdot2x^5y^6}{x^5 \cdot 25x^7y^{10}} \]

  11. phi
    • one year ago
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    notice you have x^5 in the top and in the bottom. they "cancel out" (anything divided by itself is 1) so you have \[ -\frac{5xy^2\cdot2x^5y^6}{x^5 \cdot 25x^7y^{10}} = -\frac{5xy^2\cdot2y^6}{25x^7y^{10}}\]

  12. phi
    • one year ago
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    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.

  13. Destinyyyy
    • one year ago
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    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

  14. Destinyyyy
    • one year ago
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    And then minus the exponents and all.

  15. Destinyyyy
    • one year ago
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    So I now have - 2/5

  16. phi
    • one year ago
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    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*

  17. phi
    • one year ago
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    *** 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) ?

  18. Destinyyyy
    • one year ago
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    Um okay?

  19. Destinyyyy
    • one year ago
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    Yes because of -6

  20. phi
    • one year ago
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    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 \[ - \frac{2}{5} \]

  21. phi
    • one year ago
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    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)

  22. phi
    • one year ago
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    is it clear how to simplify the x's or is it confusing?

  23. Destinyyyy
    • one year ago
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    So your talking about combining then but to try to divide first..

  24. Destinyyyy
    • one year ago
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    Do you mean subtract??

  25. phi
    • one year ago
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    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. \[ \frac{x\cdot x\cdot x\cdot x\cdot x}{ x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}\]

  26. Destinyyyy
    • one year ago
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    I have this-- - 2y^2x^-2/ 5x^-4 y^-4

  27. phi
    • one year ago
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    every time you have an "x" up top and "x" down below, they cancel out so just cancel them out in pairs.

  28. Destinyyyy
    • one year ago
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    Final answer- - 2/ 5x^6y^2

  29. phi
    • one year ago
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    what do you get for \[ \frac{x\cdot x^5}{x^5\cdot x^7} \]?

  30. phi
    • one year ago
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    I would try to keep the exponents positive (less confusing) \[ \frac{x\cdot \cancel{x^5}}{\cancel{x^5}\cdot x^7} = \frac{x}{ x^7}= \frac{1}{x^6}\]

  31. Destinyyyy
    • one year ago
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    Thank you for taking away 40 minutes of my time that I needed.

  32. Destinyyyy
    • one year ago
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    This question should of taken less then 5 minutes to solve.

  33. Destinyyyy
    • one year ago
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    Thank you for explaining things. But I did not need that. All I needed was a refresher. Im studying for my final exam.

  34. phi
    • one year ago
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    oops \[ -\frac{2}{5} \frac{1}{x^6y^2}\]

  35. Destinyyyy
    • one year ago
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    I figured that out 6 minutes ago..

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