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## anonymous one year ago what is x^2/3 -64=0

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1. zepdrix

$\large\rm x^{2/3}-64=0$Add 64,$\large\rm x^{2/3}=64$Now to deal with the exponent...

2. 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. $$\large\rm (x^2)^{1/2}=|x|$$

3. 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,$\large\rm \left(x^{2/3}\right)^{3/2}=64^{3/2}$

4. zepdrix

$\large\rm |x|=64^{3/2}$$\large\rm x=\pm 64^{3/2}$

5. zepdrix

Hopefully I was reading your initial problem correctly D: It wasn't this, right? $$\large\rm \frac{x^2}{3}-64=0$$

6. anonymous

thanks :)

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