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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.
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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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hey 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
 one year ago
Best ResponseYou've already chosen the best response.1Here 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?\[\Large\rm \left(x^{\color{royalblue}{2}}\right)^{\color{orangered}{6}}=?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I do the second part would look like this. \[x ^{12}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=\left(3x^{\frac{7}{2}}\right)^{6}x^{12}\]Ok nice that moves things along.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Another 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
 one year ago
Best ResponseYou've already chosen the best response.1The 6 is being applied to both, I meant to say*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand. So Does three get multiplied by 6? Or does three go through the normal exponent process?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The three doesn't get "multiplied" by the 6, it gets an exponent of 6. Think of it like this maybe:dw:1433224275689:dwWe 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
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i see.so it would be some thing like this? \[3^6x ^{21}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large\rm \left(3x^{\frac{7}{2}}\right)^{6}\left(x^2\right)^{6}=3^6 x^{21} x^{12}\]Ok good good good.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Another important exponent rule:\[\Large\rm x^{\color{royalblue}{a}}\cdot x^{\color{orangered}{b}}=x^{\color{royalblue}{a}+\color{orangered}{b}}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmmm, so what's that going to do for us? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it would give us 3^6x^33

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Awesomeeee, 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
 one year ago
Best ResponseYou've already chosen the best response.0Yes that sounds about right! Thank you!
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