anonymous
  • anonymous
I need to simplify this problem with radicals.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[6x^6/\sqrt[3]{9^4}\]
precal
  • precal
\[6x^6/\sqrt[3]{9*9*9*9}\] \[6x^6/9\sqrt[3]{9}\] \[2x^6/3\sqrt[3]{9}\]
anonymous
  • anonymous
My professor had gave me an answer of \[2x^4\sqrt[3]{3^2}\]. I am trying to understand how he came to this conclusion if you can explain it for me.

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precal
  • precal
are you sure it is division?
precal
  • precal
\[\sqrt[3]{9}\] is the same as \[\sqrt[3]{3^2}\]
anonymous
  • anonymous
Yup, it is as I have given it to you.
precal
  • precal
Are you sure you copied it correctly? You would be surprised how common that occurs.
anonymous
  • anonymous
Bah, you're right. \[6x^6/\sqrt[3]{9x^4}\] I had missed a variable.
anonymous
  • anonymous
Sorry about that, he is one of the teachers that writes out his homework on a sheet a paper and makes copies of it.
precal
  • precal
ok let me do it again
precal
  • precal
\[6x^6/\left( \sqrt[3]{9x^4}\right)\] \[6x^6/\left( \sqrt[3]{9x*x*x*x}\right)\] \[6x^6/\left( x\sqrt[3]{9x}\right)\] \[6x^5/\left( \sqrt[3]{9x}\right)\]
precal
  • precal
Are you sure you wrote it correctly? We are using laws of exponents. The rules are pretty clear.

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