Solve ((3*2/9*1/2)^-2*1/3/(frac{2{3})^-2:(frac{2}{9})^-1})^-1

$$( \frac { ( 3 \cdot \frac { 2 } { 9 } \cdot \frac { 1 } { 2 } ) ^ { - 2 } \cdot \frac { 1 } { 3 } } { ( \frac { 2 } { 3 } ) ^ { - 2 } : ( \frac { 2 } { 9 } ) ^ { - 1 } } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Multiply 3 and \frac{2}{9} to get \frac{2}{3}.

$$\left(\frac{\left(\frac{2}{3}\times \frac{1}{2}\right)^{-2}\times \frac{1}{3}}{\frac{\left(\frac{2}{3}\right)^{-2}}{\left(\frac{2}{9}\right)^{-1}}}\right)^{-1}$$

Multiply \frac{2}{3} and \frac{1}{2} to get \frac{1}{3}.

$$\left(\frac{\left(\frac{1}{3}\right)^{-2}\times \frac{1}{3}}{\frac{\left(\frac{2}{3}\right)^{-2}}{\left(\frac{2}{9}\right)^{-1}}}\right)^{-1}$$

Calculate \frac{1}{3} to the power of -2 and get 9.

$$\left(\frac{9\times \frac{1}{3}}{\frac{\left(\frac{2}{3}\right)^{-2}}{\left(\frac{2}{9}\right)^{-1}}}\right)^{-1}$$

Multiply 9 and \frac{1}{3} to get 3.

$$\left(\frac{3}{\frac{\left(\frac{2}{3}\right)^{-2}}{\left(\frac{2}{9}\right)^{-1}}}\right)^{-1}$$

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\left(\frac{3}{\frac{\frac{9}{4}}{\left(\frac{2}{9}\right)^{-1}}}\right)^{-1}$$

Calculate \frac{2}{9} to the power of -1 and get \frac{9}{2}.

$$\left(\frac{3}{\frac{\frac{9}{4}}{\frac{9}{2}}}\right)^{-1}$$

Divide \frac{9}{4} by \frac{9}{2} by multiplying \frac{9}{4} by the reciprocal of \frac{9}{2}.

$$\left(\frac{3}{\frac{9}{4}\times \frac{2}{9}}\right)^{-1}$$

Multiply \frac{9}{4} and \frac{2}{9} to get \frac{1}{2}.

$$\left(\frac{3}{\frac{1}{2}}\right)^{-1}$$

Divide 3 by \frac{1}{2} by multiplying 3 by the reciprocal of \frac{1}{2}.

$$\left(3\times 2\right)^{-1}$$

Multiply 3 and 2 to get 6.

$$6^{-1}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$