anonymous
  • anonymous
What is a simpler form of the radical expression? 4^square root 81x^20 y^8
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\sqrt[4]{81x^{20}y^8}\] like that ?
anonymous
  • anonymous
\[\sqrt[4]{81x ^{20}y ^{8}}\]
anonymous
  • anonymous
yeah haha you're faster than me

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anonymous
  • anonymous
this is a lot easier than you think probably how many times does 4 go in to 20?
anonymous
  • anonymous
5
anonymous
  • anonymous
right and so \[\sqrt[4]{x^{20}}=x^5\]
anonymous
  • anonymous
using the same reasoning, what do you think \[\sqrt[4]{y^8}\]is ?
anonymous
  • anonymous
2
anonymous
  • anonymous
well actually \(y^2\) but you get the idea
anonymous
  • anonymous
and all that is left to do is find \(\sqrt[4]{81}\) make a guess
anonymous
  • anonymous
hint, it has to be small, since when you multiply it by itself 4 times you get 81
anonymous
  • anonymous
9
anonymous
  • anonymous
nope too big it is true that \(9^2=81\) but \(9^4=81\times 81\) go smaller
anonymous
  • anonymous
3
anonymous
  • anonymous
right
anonymous
  • anonymous
\[3^4=3\times 3\times 3\times 3=9\times 9=81\]
anonymous
  • anonymous
3[x^5]y^2
anonymous
  • anonymous
is that the answer?
anonymous
  • anonymous
final answer: \[\sqrt[4]{81x^{20}y^8}=3x^5y^2\]the radical is gone
anonymous
  • anonymous
yes, you don't need the parentheses though, just write them next to each other
anonymous
  • anonymous
Thank you very much!
anonymous
  • anonymous
yw wasn't even that hard was it?
anonymous
  • anonymous
no
anonymous
  • anonymous
Sorry computer froze again, thank you again @satellite73

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