Solve ((23/9/3)^-2/(frac{9{4})^2(2/5)^-1})^-1

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

Evaluate

$$\frac{245}{32}=7.65625$$

Solution Steps

Express \frac{\frac{2\times 9+3}{9}}{3} as a single fraction.

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

Multiply 2 and 9 to get 18.

$$\left(\frac{\left(\frac{18+3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Add 18 and 3 to get 21.

$$\left(\frac{\left(\frac{21}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Multiply 9 and 3 to get 27.

$$\left(\frac{\left(\frac{21}{27}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Reduce the fraction \frac{21}{27} to lowest terms by extracting and canceling out 3.

$$\left(\frac{\left(\frac{7}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

Calculate \frac{7}{9} to the power of -2 and get \frac{81}{49}.

$$\left(\frac{\frac{81}{49}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

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

$$\left(\frac{\frac{81}{49}}{\frac{81}{16}\times \left(\frac{2}{5}\right)^{-1}}\right)^{-1}$$

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

$$\left(\frac{\frac{81}{49}}{\frac{81}{16}\times \frac{5}{2}}\right)^{-1}$$

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

$$\left(\frac{\frac{81}{49}}{\frac{405}{32}}\right)^{-1}$$

Divide \frac{81}{49} by \frac{405}{32} by multiplying \frac{81}{49} by the reciprocal of \frac{405}{32}.

$$\left(\frac{81}{49}\times \frac{32}{405}\right)^{-1}$$

Multiply \frac{81}{49} and \frac{32}{405} to get \frac{32}{245}.

$$\left(\frac{32}{245}\right)^{-1}$$

Calculate \frac{32}{245} to the power of -1 and get \frac{245}{32}.

$$\frac{245}{32}$$

Factor

$$\frac{5 \cdot 7 ^ {2}}{2 ^ {5}} = 7\frac{21}{32} = 7.65625$$