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

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1. anonymous

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?