Solve 1/2-sqrt[4]{frac{81/16}}{1+sqrt[3]{8/125}}=

$$\frac { \frac { 1 } { 2 } - \sqrt[ 4 ] { \frac { 81 } { 16 } } } { 1 + \sqrt[ 3 ] { \frac { 8 } { 125 } } } =$$

Evaluate

$$-\frac{5}{7}\approx -0.714285714$$

Solution Steps

Calculate \sqrt[4]{\frac{81}{16}} and get \frac{3}{2}.

$$\frac{\frac{1}{2}-\frac{3}{2}}{1+\sqrt[3]{\frac{8}{125}}}$$

Subtract \frac{3}{2} from \frac{1}{2} to get -1.

$$\frac{-1}{1+\sqrt[3]{\frac{8}{125}}}$$

Calculate \sqrt[3]{\frac{8}{125}} and get \frac{2}{5}.

$$\frac{-1}{1+\frac{2}{5}}$$

Add 1 and \frac{2}{5} to get \frac{7}{5}.

$$\frac{-1}{\frac{7}{5}}$$

Divide -1 by \frac{7}{5} by multiplying -1 by the reciprocal of \frac{7}{5}.

$$-\frac{5}{7}$$

Factor

$$-\frac{5}{7} = -0.7142857142857143$$