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anonymous

  • one year ago

I would like to know how to simplify an equation. it's an extremely long one so i'll attach a Picture.

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  1. anonymous
    • one year ago
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  2. zepdrix
    • one year ago
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    Hey Wendy :)\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}\]We need to apply a couple of exponent rules to simplify this down.

  3. zepdrix
    • one year ago
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    Here is one of our rules,\[\Large\rm \left(x^{\color{royalblue}{a}}\right)^{\color{orangered}{b}}=x^{\color{royalblue}{a}\color{orangered}{b}}\]When we have an exponent being applied on the outside like this, we simply multiply the numbers together. Do you understand how we can apply this rule to the second part?\[\Large\rm \left(x^{\color{royalblue}{2}}\right)^{\color{orangered}{6}}=?\]

  4. anonymous
    • one year ago
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    Yes, I do the second part would look like this. \[x ^{12}\]

  5. zepdrix
    • one year ago
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    \[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=\left(3x^{\frac{7}{2}}\right)^{6}x^{12}\]Ok nice that moves things along.

  6. zepdrix
    • one year ago
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    Another thing to keep in mind... when we apply an exponent to a group of things, the exponent much be applied to EACH OF THEM. So our first bracket is actually being applied to both the 3 AND the x thing,\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6\left(x^{\frac{7}{2}}\right)^{6}x^{12}\]

  7. zepdrix
    • one year ago
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    The 6 is being applied to both, I meant to say*

  8. anonymous
    • one year ago
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    I understand. So Does three get multiplied by 6? Or does three go through the normal exponent process?

  9. zepdrix
    • one year ago
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    The three doesn't get "multiplied" by the 6, it gets an exponent of 6. Think of it like this maybe:|dw:1433224275689:dw|We again apply our exponent multiplication rule, but very carefully. I was trying to avoid doing these two steps at once like this, but maybe we can try.

  10. anonymous
    • one year ago
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    oh ok i see.so it would be some thing like this? \[3^6x ^{21}\]

  11. zepdrix
    • one year ago
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    \[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6 x^{21} x^{12}\]Ok good good good.

  12. zepdrix
    • one year ago
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    Another important exponent rule:\[\Large\rm x^{\color{royalblue}{a}}\cdot x^{\color{orangered}{b}}=x^{\color{royalblue}{a}+\color{orangered}{b}}\]

  13. zepdrix
    • one year ago
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    Hmmm, so what's that going to do for us? :)

  14. anonymous
    • one year ago
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    it would give us 3^6x^33

  15. zepdrix
    • one year ago
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    Awesomeeee, good job dude! Maybe expand out the power of 3 as a final step. But it's not totally necessary. I think it's 729 or something.

  16. anonymous
    • one year ago
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    Yes that sounds about right! Thank you!

  17. zepdrix
    • one year ago
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    np

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