Final answer to the problem
$\left(\frac{3}{a-2}+\frac{-\sqrt[3]{a}}{\sqrt[3]{a^{4}}-\sqrt[3]{a}}\right)^{-1}+\frac{-3a+2}{1-2a}$
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Step-by-step Solution
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1
Simplify $\sqrt[3]{a^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{3}$
$\left(\frac{3}{a-2}+\frac{-\sqrt[3]{a}}{a^{4\frac{1}{3}}-\sqrt[3]{a}}\right)^{-1}+\frac{-\left(3a-2\right)}{1-2a}$
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$\left(\frac{3}{a-2}+\frac{-\sqrt[3]{a}}{a^{4\frac{1}{3}}-\sqrt[3]{a}}\right)^{-1}+\frac{-\left(3a-2\right)}{1-2a}$
Learn how to solve factor problems step by step online. Factor the expression (3/(a-2)+(-a^1/3)/(a^4^1/3-a^1/3))^(-1)+(-(3a-2))/(1-2a). Simplify \sqrt[3]{a^4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{3}. Multiply 4 times \frac{1}{3}. Simplify the product -(3a-2).
Final answer to the problem
$\left(\frac{3}{a-2}+\frac{-\sqrt[3]{a}}{\sqrt[3]{a^{4}}-\sqrt[3]{a}}\right)^{-1}+\frac{-3a+2}{1-2a}$