Solve (frac{1/27)^frac{4{3}}}{(16/81)^1/4(-27/64)^1/3}

$$\frac { ( \frac { 1 } { 27 } ) ^ { \frac { 4 } { 3 } } } { ( \frac { 16 } { 81 } ) ^ { 1 / 4 } ( - \frac { 27 } { 64 } ) ^ { 1 / 3 } }$$

Evaluate

$$-\frac{2}{81}\approx -0.024691358$$

Solution Steps

Calculate \frac{1}{27} to the power of \frac{4}{3} and get \frac{1}{81}.

$$\frac{\frac{1}{81}}{\left(\frac{16}{81}\right)^{\frac{1}{4}}\left(-\frac{27}{64}\right)^{\frac{1}{3}}}$$

Calculate \frac{16}{81} to the power of \frac{1}{4} and get \frac{2}{3}.

$$\frac{\frac{1}{81}}{\frac{2}{3}\left(-\frac{27}{64}\right)^{\frac{1}{3}}}$$

Calculate -\frac{27}{64} to the power of \frac{1}{3} and get -\frac{3}{4}.

$$\frac{\frac{1}{81}}{\frac{2}{3}\left(-\frac{3}{4}\right)}$$

Multiply \frac{2}{3} and -\frac{3}{4} to get -\frac{1}{2}.

$$\frac{\frac{1}{81}}{-\frac{1}{2}}$$

Divide \frac{1}{81} by -\frac{1}{2} by multiplying \frac{1}{81} by the reciprocal of -\frac{1}{2}.

$$\frac{1}{81}\left(-2\right)$$

Multiply \frac{1}{81} and -2 to get -\frac{2}{81}.

$$-\frac{2}{81}$$

Factor

$$-\frac{2}{81} = -0.024691358024691357$$