Solve (27^-frac{2{3}}-1/4643/2)^-1

$$( 27 ^ { - \frac { 2 } { 3 } } - \frac { 1 } { 4 } 64 \frac { 3 } { 2 } ) ^ { - 1 }$$

Evaluate

$$-\frac{72}{1171}\approx -0.061485909$$

Solution Steps

Calculate 27 to the power of -\frac{2}{3} and get \frac{1}{9}.

$$\left(\frac{1}{9}-\frac{1}{4}\times \frac{64\times 2+3}{2}\right)^{-1}$$

Multiply 64 and 2 to get 128.

$$\left(\frac{1}{9}-\frac{1}{4}\times \frac{128+3}{2}\right)^{-1}$$

Add 128 and 3 to get 131.

$$\left(\frac{1}{9}-\frac{1}{4}\times \frac{131}{2}\right)^{-1}$$

Multiply \frac{1}{4} and \frac{131}{2} to get \frac{131}{8}.

$$\left(\frac{1}{9}-\frac{131}{8}\right)^{-1}$$

Subtract \frac{131}{8} from \frac{1}{9} to get -\frac{1171}{72}.

$$\left(-\frac{1171}{72}\right)^{-1}$$

Calculate -\frac{1171}{72} to the power of -1 and get -\frac{72}{1171}.

$$-\frac{72}{1171}$$

Factor

$$-\frac{72}{1171} = -0.06148590947907771$$