anonymous
  • anonymous
I would like to know how to simplify an equation. it's an extremely long one so i'll attach a Picture.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
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?\[\Large\rm \left(x^{\color{royalblue}{2}}\right)^{\color{orangered}{6}}=?\]

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anonymous
  • anonymous
Yes, I do the second part would look like this. \[x ^{12}\]
zepdrix
  • zepdrix
\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=\left(3x^{\frac{7}{2}}\right)^{6}x^{12}\]Ok nice that moves things along.
zepdrix
  • zepdrix
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,\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6\left(x^{\frac{7}{2}}\right)^{6}x^{12}\]
zepdrix
  • zepdrix
The 6 is being applied to both, I meant to say*
anonymous
  • anonymous
I understand. So Does three get multiplied by 6? Or does three go through the normal exponent process?
zepdrix
  • zepdrix
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.
anonymous
  • anonymous
oh ok i see.so it would be some thing like this? \[3^6x ^{21}\]
zepdrix
  • zepdrix
\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6 x^{21} x^{12}\]Ok good good good.
zepdrix
  • zepdrix
Another important exponent rule:\[\Large\rm x^{\color{royalblue}{a}}\cdot x^{\color{orangered}{b}}=x^{\color{royalblue}{a}+\color{orangered}{b}}\]
zepdrix
  • zepdrix
Hmmm, so what's that going to do for us? :)
anonymous
  • anonymous
it would give us 3^6x^33
zepdrix
  • zepdrix
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.
anonymous
  • anonymous
Yes that sounds about right! Thank you!
zepdrix
  • zepdrix
np

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