1. Factoring Differences of Cubes

I'm having trouble factoring this particular difference of cubes. Could someone please show me step by step how to approach this?

The expression is:

(1/512x)^9 -512

Thanks!!

2. Originally Posted by MATHDUDE2
I'm having trouble factoring this particular difference of cubes. Could someone please show me step by step how to approach this?

The expression is:

(1/512x)^9 -512

Thanks!!
We need to use the exponential law that (x^a)^b=x^{ab}

$\left[\left( \frac{1}{512x} \right)^3\right]^3-(2^3)^3=...$

So we can identify $a=\left( \frac{1}{512x} \right)^3$ and $b=2^3=8$
$a^3-b^3=(a-b)(a^2-ab+b^2)$ so just plug into the formula from here

3. thanks!