Solve (-3/4+1/5)*(-3/11-1/2):(-frac{1}{4}-frac{3}{10}*2):[(-frac{1}{2})^-6]^4-frac{1}{2^25}

$$( - \frac { 3 } { 4 } + \frac { 1 } { 5 } ) \cdot ( - \frac { 3 } { 11 } - \frac { 1 } { 2 } ) : ( - \frac { 1 } { 4 } - \frac { 3 } { 10 } \cdot 2 ) : [ ( - \frac { 1 } { 2 } ) ^ { - 6 } ] ^ { 4 } - \frac { 1 } { 2 ^ { 25 } }$$

Evaluate

$$-\frac{1}{16777216}=-0.00000006$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$\frac{\frac{\left(-\frac{3}{4}+\frac{1}{5}\right)\left(-\frac{3}{11}-\frac{1}{2}\right)}{-\frac{1}{4}-\frac{3}{10}\times 2}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Add -\frac{3}{4} and \frac{1}{5} to get -\frac{11}{20}.

$$\frac{\frac{-\frac{11}{20}\left(-\frac{3}{11}-\frac{1}{2}\right)}{-\frac{1}{4}-\frac{3}{10}\times 2}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Subtract \frac{1}{2} from -\frac{3}{11} to get -\frac{17}{22}.

$$\frac{\frac{-\frac{11}{20}\left(-\frac{17}{22}\right)}{-\frac{1}{4}-\frac{3}{10}\times 2}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Multiply -\frac{11}{20} and -\frac{17}{22} to get \frac{17}{40}.

$$\frac{\frac{\frac{17}{40}}{-\frac{1}{4}-\frac{3}{10}\times 2}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Multiply \frac{3}{10} and 2 to get \frac{3}{5}.

$$\frac{\frac{\frac{17}{40}}{-\frac{1}{4}-\frac{3}{5}}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Subtract \frac{3}{5} from -\frac{1}{4} to get -\frac{17}{20}.

$$\frac{\frac{\frac{17}{40}}{-\frac{17}{20}}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Divide \frac{17}{40} by -\frac{17}{20} by multiplying \frac{17}{40} by the reciprocal of -\frac{17}{20}.

$$\frac{\frac{17}{40}\left(-\frac{20}{17}\right)}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Multiply \frac{17}{40} and -\frac{20}{17} to get -\frac{1}{2}.

$$\frac{-\frac{1}{2}}{\left(-\frac{1}{2}\right)^{-24}}-\frac{1}{2^{25}}$$

Calculate -\frac{1}{2} to the power of -24 and get 16777216.

$$\frac{-\frac{1}{2}}{16777216}-\frac{1}{2^{25}}$$

Express \frac{-\frac{1}{2}}{16777216} as a single fraction.

$$\frac{-1}{2\times 16777216}-\frac{1}{2^{25}}$$

Multiply 2 and 16777216 to get 33554432.

$$\frac{-1}{33554432}-\frac{1}{2^{25}}$$

Fraction \frac{-1}{33554432} can be rewritten as -\frac{1}{33554432} by extracting the negative sign.

$$-\frac{1}{33554432}-\frac{1}{2^{25}}$$

Calculate 2 to the power of 25 and get 33554432.

$$-\frac{1}{33554432}-\frac{1}{33554432}$$

Subtract \frac{1}{33554432} from -\frac{1}{33554432} to get -\frac{1}{16777216}.

$$-\frac{1}{16777216}$$

Factor

$$-\frac{1}{16777216} = -5.9604644775390625 \times 10^{-8}$$