What is the answer to x^{-3}=8 ?

The answer to x^{-3}=8 is x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i

Solve for x: x^{-3}=8

The solution is x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i

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x^{- 3} = 8

x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Solution steps

x^{- 3} = 8

Refine

\frac{1}{x ^{3}} = 8

Multiply both sides by

x^{3}

1 = 8 x^{3}

Solve

1 = 8 x^{3} : x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

x^{2} + 3 x + 2 = \frac{2}{( x ^{2} + 3 x + 3 )}

(\frac{x}{( x - 1 )})^{2} + 4 (\frac{x}{( x - 1 )}) + 2 = 0

\frac{( - \frac{4}{3} ) ^{- 2}}{x} = (\frac{8}{15})^{- 1}

x + \frac{3}{x} - 2 - 1 - \frac{x}{x} = \frac{41}{4}

\frac{3}{4 \cdot x ^{2} - 8 x + 3} = 0

What is the answer to x^{-3}=8 ?
The answer to x^{-3}=8 is x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i
Solve for x: x^{-3}=8
The solution is x= 1/2 ,x=-1/4+(sqrt(3))/4 i,x=-1/4-(sqrt(3))/4 i