Question

Can someone please help me step by step with this problem?
x^(-2/3) (2-x)^2 - 6x^1/3 (2-x)

Answer 1

Without knowing exactly what you're trying to do, we can't help much. I'd guess you're wanting to simplify the given expression.
\[x^{-2/3}(2-x)^2-6x^{1/3}(2-x)\]
For starters, there's a common factor of \(2-x\), so let's pull that out:
\[(2-x)\left[x^{-2/3}(2-x)-6x^{1/3}\right]\]
Next, notice that \(-\dfrac{2}{3}=-\dfrac{3}{3}+\dfrac{1}{3}\). Since \(x^{a+b}=x^ax^b\), this means that \(x^{-2/3}=x^{-3/3}x^{1/3}=x^{-1}x^{1/3}\), and so the two bracketed terms share another common factor of \(x^{1/3}\). Pulling that out gives
\[x^{1/3}(2-x)\left[x^{-1}(2-x)-6\right]\]
What else can you do?