Solve (-2/3)^-3divx=(9/8)^2

$$( \frac { - 2 } { 3 } ) ^ { - 3 } \div x = ( \frac { 9 } { 8 } ) ^ { 2 }$$

Solve for x

$$x = -\frac{8}{3} = -2\frac{2}{3} \approx -2.666666667$$

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 x.

$$\left(\frac{-2}{3}\right)^{-3}=x\times \left(\frac{9}{8}\right)^{2}$$

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

$$\left(-\frac{2}{3}\right)^{-3}=x\times \left(\frac{9}{8}\right)^{2}$$

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

$$-\frac{27}{8}=x\times \left(\frac{9}{8}\right)^{2}$$

Calculate \frac{9}{8} to the power of 2 and get \frac{81}{64}.

$$-\frac{27}{8}=x\times \frac{81}{64}$$

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

$$x\times \frac{81}{64}=-\frac{27}{8}$$

Multiply both sides by \frac{64}{81}, the reciprocal of \frac{81}{64}.

$$x=-\frac{27}{8}\times \frac{64}{81}$$

Multiply -\frac{27}{8} and \frac{64}{81} to get -\frac{8}{3}.

$$x=-\frac{8}{3}$$