Solve (1/8-frac{1/4-4)-2^{5}*{[(1+1/3)^{-4}*(1-1/4)^-4+frac{2}{3}]^-3*(-frac{10}{3})^3*frac{1}{64}}}{-[5+(-frac{1}{2})^-4]*(-frac{1}{3})+frac{12}{5}*(1+frac{1}{4})-frac{75}{8}}

$$\frac { ( \frac { 1 } { 8 } - \frac { 1 } { 4 } - 4 ) - 2 ^ { 5 } \cdot \{ [ ( 1 + \frac { 1 } { 3 } ) ^ { - 4 } \cdot ( 1 - \frac { 1 } { 4 } ) ^ { - 4 } + \frac { 2 } { 3 } ] ^ { - 3 } \cdot ( - \frac { 10 } { 3 } ) ^ { 3 } \cdot \frac { 1 } { 64 } \} } { - [ 5 + ( - \frac { 1 } { 2 } ) ^ { - 4 } ] \cdot ( - \frac { 1 } { 3 } ) + \frac { 12 } { 5 } \cdot ( 1 + \frac { 1 } { 4 } ) - \frac { 75 } { 8 } }$$

Evaluate

$$-\frac{1}{5}=-0.2$$

Solution Steps

Subtract \frac{1}{4} from \frac{1}{8} to get -\frac{1}{8}.

$$\frac{-\frac{1}{8}-4-2^{5}\left(\left(1+\frac{1}{3}\right)^{-4}\left(1-\frac{1}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Subtract 4 from -\frac{1}{8} to get -\frac{33}{8}.

$$\frac{-\frac{33}{8}-2^{5}\left(\left(1+\frac{1}{3}\right)^{-4}\left(1-\frac{1}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{-\frac{33}{8}-32\left(\left(1+\frac{1}{3}\right)^{-4}\left(1-\frac{1}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{-\frac{33}{8}-32\left(\left(\frac{4}{3}\right)^{-4}\left(1-\frac{1}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Calculate \frac{4}{3} to the power of -4 and get \frac{81}{256}.

$$\frac{-\frac{33}{8}-32\left(\frac{81}{256}\left(1-\frac{1}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

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

$$\frac{-\frac{33}{8}-32\left(\frac{81}{256}\times \left(\frac{3}{4}\right)^{-4}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Calculate \frac{3}{4} to the power of -4 and get \frac{256}{81}.

$$\frac{-\frac{33}{8}-32\left(\frac{81}{256}\times \frac{256}{81}+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Multiply \frac{81}{256} and \frac{256}{81} to get 1.

$$\frac{-\frac{33}{8}-32\left(1+\frac{2}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$\frac{-\frac{33}{8}-32\times \left(\frac{5}{3}\right)^{-3}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Calculate \frac{5}{3} to the power of -3 and get \frac{27}{125}.

$$\frac{-\frac{33}{8}-32\times \frac{27}{125}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Multiply 32 and \frac{27}{125} to get \frac{864}{125}.

$$\frac{-\frac{33}{8}-\frac{864}{125}\left(-\frac{10}{3}\right)^{3}\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Calculate -\frac{10}{3} to the power of 3 and get -\frac{1000}{27}.

$$\frac{-\frac{33}{8}-\frac{864}{125}\left(-\frac{1000}{27}\right)\times \frac{1}{64}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Multiply \frac{864}{125} and -\frac{1000}{27} to get -256.

$$\frac{-\frac{33}{8}-\left(-256\times \frac{1}{64}\right)}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Multiply -256 and \frac{1}{64} to get -4.

$$\frac{-\frac{33}{8}-\left(-4\right)}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

The opposite of -4 is 4.

$$\frac{-\frac{33}{8}+4}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Add -\frac{33}{8} and 4 to get -\frac{1}{8}.

$$\frac{-\frac{1}{8}}{\left(-\left(5+\left(-\frac{1}{2}\right)^{-4}\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

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

$$\frac{-\frac{1}{8}}{\left(-\left(5+16\right)\right)\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Add 5 and 16 to get 21.

$$\frac{-\frac{1}{8}}{-21\left(-\frac{1}{3}\right)+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Multiply -21 and -\frac{1}{3} to get 7.

$$\frac{-\frac{1}{8}}{7+\frac{12}{5}\left(1+\frac{1}{4}\right)-\frac{75}{8}}$$

Add 1 and \frac{1}{4} to get \frac{5}{4}.

$$\frac{-\frac{1}{8}}{7+\frac{12}{5}\times \frac{5}{4}-\frac{75}{8}}$$

Multiply \frac{12}{5} and \frac{5}{4} to get 3.

$$\frac{-\frac{1}{8}}{7+3-\frac{75}{8}}$$

Add 7 and 3 to get 10.

$$\frac{-\frac{1}{8}}{10-\frac{75}{8}}$$

Subtract \frac{75}{8} from 10 to get \frac{5}{8}.

$$\frac{-\frac{1}{8}}{\frac{5}{8}}$$

Divide -\frac{1}{8} by \frac{5}{8} by multiplying -\frac{1}{8} by the reciprocal of \frac{5}{8}.

$$-\frac{1}{8}\times \frac{8}{5}$$

Multiply -\frac{1}{8} and \frac{8}{5} to get -\frac{1}{5}.

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

Factor

$$-\frac{1}{5} = -0.2$$