Solve ((2*3/9div3)^-2/(frac{9{4})^2*(2/5)^-1})^-1

$$( \frac { ( 2 \times \frac { 3 } { 9 } \div 3 ) ^ { - 2 } } { ( \frac { 9 } { 4 } ) ^ { 2 } \times ( \frac { 2 } { 5 } ) ^ { - 1 } } ) ^ { - 1 }$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\left(\frac{\left(\frac{2\times \frac{1}{3}}{3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

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

$$\left(\frac{\left(\frac{\frac{2}{3}}{3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Express \frac{\frac{2}{3}}{3} as a single fraction.

$$\left(\frac{\left(\frac{2}{3\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Multiply 3 and 3 to get 9.

$$\left(\frac{\left(\frac{2}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Calculate \frac{2}{9} to the power of -2 and get \frac{81}{4}.

$$\left(\frac{\frac{81}{4}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$\left(\frac{\frac{81}{4}}{\frac{81}{16}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Calculate \frac{2}{5} to the power of -1 and get \frac{5}{2}.

$$\left(\frac{\frac{81}{4}}{\frac{81}{16}\times \frac{5}{2}}\right)^{-1}$$

Multiply \frac{81}{16} and \frac{5}{2} to get \frac{405}{32}.

$$\left(\frac{\frac{81}{4}}{\frac{405}{32}}\right)^{-1}$$

Divide \frac{81}{4} by \frac{405}{32} by multiplying \frac{81}{4} by the reciprocal of \frac{405}{32}.

$$\left(\frac{81}{4}\times \frac{32}{405}\right)^{-1}$$

Multiply \frac{81}{4} and \frac{32}{405} to get \frac{8}{5}.

$$\left(\frac{8}{5}\right)^{-1}$$

Calculate \frac{8}{5} to the power of -1 and get \frac{5}{8}.

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$