Question

what is x^2/3 -64=0

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

thanks :)