Solve [3/5]^-1-1/6/sqrt[3]{frac{3{4}-1+1/8}}*frac{10}{[frac{3}{2}]^-2+frac{2}{3}}

$$\frac { [ \frac { 3 } { 5 } ] ^ { - 1 } - \frac { 1 } { 6 } } { \sqrt[ 3 ] { \frac { 3 } { 4 } - 1 + \frac { 1 } { 8 } } } \cdot \frac { 10 } { [ \frac { 3 } { 2 } ] ^ { - 2 } + \frac { 2 } { 3 } }$$

Evaluate

$$-27$$

Solution Steps

Calculate \frac{3}{5} to the power of -1 and get \frac{5}{3}.

$$\frac{\frac{5}{3}-\frac{1}{6}}{\sqrt[3]{\frac{3}{4}-1+\frac{1}{8}}}\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Subtract \frac{1}{6} from \frac{5}{3} to get \frac{3}{2}.

$$\frac{\frac{3}{2}}{\sqrt[3]{\frac{3}{4}-1+\frac{1}{8}}}\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Subtract 1 from \frac{3}{4} to get -\frac{1}{4}.

$$\frac{\frac{3}{2}}{\sqrt[3]{-\frac{1}{4}+\frac{1}{8}}}\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Add -\frac{1}{4} and \frac{1}{8} to get -\frac{1}{8}.

$$\frac{\frac{3}{2}}{\sqrt[3]{-\frac{1}{8}}}\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

$$\frac{\frac{3}{2}}{-\frac{1}{2}}\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Divide \frac{3}{2} by -\frac{1}{2} by multiplying \frac{3}{2} by the reciprocal of -\frac{1}{2}.

$$\frac{3}{2}\left(-2\right)\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

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

$$-3\times \frac{10}{\left(\frac{3}{2}\right)^{-2}+\frac{2}{3}}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$-3\times \frac{10}{\frac{4}{9}+\frac{2}{3}}$$

Add \frac{4}{9} and \frac{2}{3} to get \frac{10}{9}.

$$-3\times \frac{10}{\frac{10}{9}}$$

Divide 10 by \frac{10}{9} by multiplying 10 by the reciprocal of \frac{10}{9}.

$$-3\times 10\times \frac{9}{10}$$

Multiply 10 and \frac{9}{10} to get 9.

$$-3\times 9$$

Multiply -3 and 9 to get -27.

$$-27$$

Factor

$$-27$$