Solve ((4*6/9*1/3)^-2/(frac{9{4})^2*(2/5)^-1})

$$( \frac { ( 4 * \frac { 6 } { 9 } * \frac { 1 } { 3 } ) ^ { - 2 } } { ( \frac { 9 } { 4 } ) ^ { 2 } * ( \frac { 2 } { 5 } ) ^ { - 1 } } )$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

Multiply 4 and \frac{2}{3} to get \frac{8}{3}.

$$\frac{\left(\frac{8}{3}\times \frac{1}{3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}$$

Multiply \frac{8}{3} and \frac{1}{3} to get \frac{8}{9}.

$$\frac{\left(\frac{8}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}$$

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

$$\frac{\frac{81}{64}}{\left(\frac{9}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{-1}}$$

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

$$\frac{\frac{81}{64}}{\frac{81}{16}\times \left(\frac{2}{5}\right)^{-1}}$$

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

$$\frac{\frac{81}{64}}{\frac{81}{16}\times \frac{5}{2}}$$

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

$$\frac{\frac{81}{64}}{\frac{405}{32}}$$

Divide \frac{81}{64} by \frac{405}{32} by multiplying \frac{81}{64} by the reciprocal of \frac{405}{32}.

$$\frac{81}{64}\times \frac{32}{405}$$

Multiply \frac{81}{64} and \frac{32}{405} to get \frac{1}{10}.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$