What is the answer to 2/3 x^{-1/3}=1 ?

The answer to 2/3 x^{-1/3}=1 is x= 8/27

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2/3 x^{-1/3}=1

\frac{2}{3} x^{- \frac{1}{3}} = 1

x = \frac{8}{27}

Decimal Notation

x = 0.29629 \dots

Solution steps

\frac{2}{3} x^{- \frac{1}{3}} = 1

Multiply both sides by

3

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

Simplify

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

Expand

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

\frac{2}{x ^{\frac{1}{3}}} = 3

Take both sides of the equation to the power of

3 : \frac{8}{x} = 27

\frac{8}{x} = 27

Solve

\frac{8}{x} = 27 : x = \frac{8}{27}

x = \frac{8}{27}

Verify Solutions:

x = \frac{8}{27}

True

The solution is

x = \frac{8}{27}

x - 1 + x - 7 = 2 x - 3

x - 2 = x - 2

9 x + 63 = x + 7

\frac{5 x - 8}{3 x ^{\frac{1}{3}}} = 0