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  • 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
    • one year ago
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    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?

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