What is x^{1/3}(4x^{2/3}-2x^{-1/3}) ?

The solution to x^{1/3}(4x^{2/3}-2x^{-1/3}) is x^{1/3}(4x^{2/3}-2/(x^{1/3)})

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simplify x^{1/3}(4x^{2/3}-2x^{-1/3})

simplify

x^{\frac{1}{3}} (4 x^{\frac{2}{3}} - 2 x^{- \frac{1}{3}})

x^{\frac{1}{3}} (4 x^{\frac{2}{3}} - \frac{2}{x ^{\frac{1}{3}}})

Solution steps

x^{\frac{1}{3}} (4 x^{\frac{2}{3}} - 2 x^{- \frac{1}{3}})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- \frac{1}{3}} = \frac{1}{x ^{\frac{1}{3}}}

= x^{\frac{1}{3}} (4 x^{\frac{2}{3}} - 2 \cdot \frac{1}{x ^{\frac{1}{3}}})

Simplify

2 \cdot \frac{1}{x ^{\frac{1}{3}}} : \frac{2}{x ^{\frac{1}{3}}}

= x^{\frac{1}{3}} (4 x^{\frac{2}{3}} - \frac{2}{x ^{\frac{1}{3}}})

4 x^{2} - 1 + x^{3} - 3 x^{2} + 6 x - 2

7 \times 12

4 - \frac{1}{8}

(- 3^{2})^{3}

- 25 + - 121 - - 9

What is x^{1/3}(4x^{2/3}-2x^{-1/3}) ?
The solution to x^{1/3}(4x^{2/3}-2x^{-1/3}) is x^{1/3}(4x^{2/3}-2/(x^{1/3)})