Solve {11-[2/3*(1/2)^{2}+(2-2/3*3/2^0)^3+(5-sqrt[3]{frac{1}{8}})]:frac{14}{3^3}}^2

$$\{ 11 - [ \frac { 2 } { 3 } \cdot ( \frac { 1 } { 2 } ) ^ { 2 } + ( 2 - \frac { 2 } { 3 } \cdot \frac { 3 } { 2 ^ { 0 } } ) ^ { 3 } + ( 5 - \sqrt[ 3 ] { \frac { 1 } { 8 } } ) ] : \frac { 14 } { 3 ^ { 3 } } \} ^ { 2 }$$

Evaluate

$$4$$

Solution Steps

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

$$\left(11-\frac{\frac{2}{3}\times \frac{1}{4}+\left(2-\frac{2}{3}\times \frac{3}{2^{0}}\right)^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Multiply \frac{2}{3} and \frac{1}{4} to get \frac{1}{6}.

$$\left(11-\frac{\frac{1}{6}+\left(2-\frac{2}{3}\times \frac{3}{2^{0}}\right)^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Calculate 2 to the power of 0 and get 1.

$$\left(11-\frac{\frac{1}{6}+\left(2-\frac{2}{3}\times \frac{3}{1}\right)^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Anything divided by one gives itself.

$$\left(11-\frac{\frac{1}{6}+\left(2-\frac{2}{3}\times 3\right)^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

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

$$\left(11-\frac{\frac{1}{6}+\left(2-2\right)^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Subtract 2 from 2 to get 0.

$$\left(11-\frac{\frac{1}{6}+0^{3}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Calculate 0 to the power of 3 and get 0.

$$\left(11-\frac{\frac{1}{6}+0+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

Add \frac{1}{6} and 0 to get \frac{1}{6}.

$$\left(11-\frac{\frac{1}{6}+5-\sqrt[3]{\frac{1}{8}}}{\frac{14}{3^{3}}}\right)^{2}$$

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

$$\left(11-\frac{\frac{1}{6}+5-\frac{1}{2}}{\frac{14}{3^{3}}}\right)^{2}$$

Subtract \frac{1}{2} from 5 to get \frac{9}{2}.

$$\left(11-\frac{\frac{1}{6}+\frac{9}{2}}{\frac{14}{3^{3}}}\right)^{2}$$

Add \frac{1}{6} and \frac{9}{2} to get \frac{14}{3}.

$$\left(11-\frac{\frac{14}{3}}{\frac{14}{3^{3}}}\right)^{2}$$

Calculate 3 to the power of 3 and get 27.

$$\left(11-\frac{\frac{14}{3}}{\frac{14}{27}}\right)^{2}$$

Divide \frac{14}{3} by \frac{14}{27} by multiplying \frac{14}{3} by the reciprocal of \frac{14}{27}.

$$\left(11-\frac{14}{3}\times \frac{27}{14}\right)^{2}$$

Multiply \frac{14}{3} and \frac{27}{14} to get 9.

$$\left(11-9\right)^{2}$$

Subtract 9 from 11 to get 2.

$$2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4$$

Factor

$$2^{2}$$