anonymous
  • anonymous
what is x^2/3 -64=0
Mathematics
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anonymous
  • anonymous
what is x^2/3 -64=0
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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zepdrix
  • zepdrix
\[\large\rm x^{2/3}-64=0\]Add 64,\[\large\rm x^{2/3}=64\]Now to deal with the exponent...
zepdrix
  • zepdrix
If you were dealing with something like this: \(\large\rm \sqrt[3]{x}\) you could rewrite it like this: \(\large\rm x^{1/3}\) and to undo the root, you would raise it to the third power. \(\large\rm \left(x^{1/3}\right)^{3}=x\) If I was trying to undo an exponent from something like this: \(\large\rm x^{2}\) I would take the square root of it, which is the same as applying the 1/2 power. \(\large\rm (x^2)^{1/2}=|x|\)
zepdrix
  • zepdrix
In our problem here, we kinda want to do both of those things. We want to get rid of the 2 on the x, and the 1/3 on the x. So we'll apply a 3/2 power to each side,\[\large\rm \left(x^{2/3}\right)^{3/2}=64^{3/2}\]

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zepdrix
  • zepdrix
\[\large\rm |x|=64^{3/2}\]\[\large\rm x=\pm 64^{3/2}\]
zepdrix
  • zepdrix
Hopefully I was reading your initial problem correctly D: It wasn't this, right? \(\large\rm \frac{x^2}{3}-64=0\)
anonymous
  • anonymous
thanks :)

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