Solve (-2/3)^-3divx=(4/27)

$$( \frac { - 2 } { 3 } ) ^ { - 3 } \div x = ( \frac { 4 } { 27 } )$$

Solve for x

$$x = -\frac{729}{32} = -22\frac{25}{32} = -22.78125$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 27x, the least common multiple of x,27.

$$27\times \left(\frac{-2}{3}\right)^{-3}=4x$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$27\left(-\frac{2}{3}\right)^{-3}=4x$$

Calculate -\frac{2}{3} to the power of -3 and get -\frac{27}{8}.

$$27\left(-\frac{27}{8}\right)=4x$$

Multiply 27 and -\frac{27}{8} to get -\frac{729}{8}.

$$-\frac{729}{8}=4x$$

Swap sides so that all variable terms are on the left hand side.

$$4x=-\frac{729}{8}$$

Divide both sides by 4.

$$x=\frac{-\frac{729}{8}}{4}$$

Express \frac{-\frac{729}{8}}{4} as a single fraction.

$$x=\frac{-729}{8\times 4}$$

Multiply 8 and 4 to get 32.

$$x=\frac{-729}{32}$$

Fraction \frac{-729}{32} can be rewritten as -\frac{729}{32} by extracting the negative sign.

$$x=-\frac{729}{32}$$