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If someone could provide me with a website or link with information about this I'd be grateful but otherwise: I have the number two (with the ability to add a power) and the number $8^{-\frac{2}{3}}$, I'm supposed to express the latter number as $2^x$. I'd guess that I would find the cubed root of 8 to the power to 2 which equals 4 then divide that by 1 (it'd be a fraction $\frac{1}{\sqrt[3]{8}^2}$), but this doesn't look right. Could anyone enlighten me?

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In a question like this, the indices that are already there are not the problem - the problem is that you have 8 to the power something, and you want 2 to the power of something. So if we start by noticing that $2^3 = 8$, then we can just substitute, so $8^{-\frac{2}{3}} = (2^3)^{-\frac{2}{3}}$.

But then we can just multiply the indices, so $8^{-\frac{2}{3}} = (2^3)^{-\frac{2}{3}} = 2^{3\cdot -\frac{2}{3}} = 2^{-2}$.

Note that since the cube root of 8 is 2, this is the same as what you had.

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