Solve (2(1-1/2)+[(2)^2]^-3/-frac{3{4}-(-3)+2/5*3/8})=

$$( \frac { 2 ( 1 - \frac { 1 } { 2 } ) + [ ( 2 ) ^ { 2 } ] ^ { - 3 } } { - \frac { 3 } { 4 } - ( - 3 ) + \frac { 2 } { 5 } \cdot \frac { 3 } { 8 } } ) =$$

Evaluate

$$\frac{325}{768}\approx 0.423177083$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

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

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

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

Multiply 2 and \frac{1}{2} to get 1.

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

Calculate 2 to the power of -6 and get \frac{1}{64}.

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

Add 1 and \frac{1}{64} to get \frac{65}{64}.

$$\frac{\frac{65}{64}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}$$

The opposite of -3 is 3.

$$\frac{\frac{65}{64}}{-\frac{3}{4}+3+\frac{2}{5}\times \frac{3}{8}}$$

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

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{2}{5}\times \frac{3}{8}}$$

Multiply \frac{2}{5} and \frac{3}{8} to get \frac{3}{20}.

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{3}{20}}$$

Add \frac{9}{4} and \frac{3}{20} to get \frac{12}{5}.

$$\frac{\frac{65}{64}}{\frac{12}{5}}$$

Divide \frac{65}{64} by \frac{12}{5} by multiplying \frac{65}{64} by the reciprocal of \frac{12}{5}.

$$\frac{65}{64}\times \frac{5}{12}$$

Multiply \frac{65}{64} and \frac{5}{12} to get \frac{325}{768}.

$$\frac{325}{768}$$

Factor

$$\frac{5 ^ {2} \cdot 13}{2 ^ {8} \cdot 3} = 0.4231770833333333$$