Solve 0.4-1/2+{left(frac{5/6right)}^-2}{{left(1/2^-1right)}^-1}+1.13410^-6/5.6710^-7-0.1^2-{left(frac{1-frac{1}{2}}{frac{-1}{4}-2}right)}^-1

$$\frac{ 0.4 \frac{ -1 }{ 2 } + { \left( \frac{ 5 }{ 6 } \right) }^{ -2 } }{ { \left( \frac{ 1 }{ { 2 }^{ -1 } } \right) }^{ -1 } } + \frac{ 1.134 { 10 }^{ -6 } }{ 5.67 { 10 }^{ -7 } } { -0.1 }^{ 2 } - { \left( \frac{ 1- \frac{ 1 }{ 2 } }{ \frac{ -1 }{ 4 } -2 } \right) }^{ -1 }$$

Evaluate

$$7$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{0.4\left(-\frac{1}{2}\right)+\left(\frac{5}{6}\right)^{-2}}{\left(\frac{1}{2^{-1}}\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Multiply 0.4 and -\frac{1}{2} to get -\frac{1}{5}.

$$\frac{-\frac{1}{5}+\left(\frac{5}{6}\right)^{-2}}{\left(\frac{1}{2^{-1}}\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Calculate \frac{5}{6} to the power of -2 and get \frac{36}{25}.

$$\frac{-\frac{1}{5}+\frac{36}{25}}{\left(\frac{1}{2^{-1}}\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Add -\frac{1}{5} and \frac{36}{25} to get \frac{31}{25}.

$$\frac{\frac{31}{25}}{\left(\frac{1}{2^{-1}}\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

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

$$\frac{\frac{31}{25}}{\left(\frac{1}{\frac{1}{2}}\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

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

$$\frac{\frac{31}{25}}{\left(1\times 2\right)^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{31}{25}}{2^{-1}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

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

$$\frac{\frac{31}{25}}{\frac{1}{2}}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Divide \frac{31}{25} by \frac{1}{2} by multiplying \frac{31}{25} by the reciprocal of \frac{1}{2}.

$$\frac{31}{25}\times 2+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Multiply \frac{31}{25} and 2 to get \frac{62}{25}.

$$\frac{62}{25}+\frac{1.134\times 10^{-6}}{5.67\times 10^{-7}}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{62}{25}+\frac{1.134\times 10^{1}}{5.67}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{62}{25}+\frac{1.134\times 10}{5.67}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Multiply 1.134 and 10 to get 11.34.

$$\frac{62}{25}+\frac{11.34}{5.67}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Expand \frac{11.34}{5.67} by multiplying both numerator and the denominator by 100.

$$\frac{62}{25}+\frac{1134}{567}\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Divide 1134 by 567 to get 2.

$$\frac{62}{25}+2\left(-0.1\right)^{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Calculate -0.1 to the power of 2 and get 0.01.

$$\frac{62}{25}+2\times 0.01-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Multiply 2 and 0.01 to get 0.02.

$$\frac{62}{25}+0.02-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Add \frac{62}{25} and 0.02 to get \frac{5}{2}.

$$\frac{5}{2}-\left(\frac{1-\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

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

$$\frac{5}{2}-\left(\frac{\frac{1}{2}}{\frac{-1}{4}-2}\right)^{-1}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{5}{2}-\left(\frac{\frac{1}{2}}{-\frac{1}{4}-2}\right)^{-1}$$

Subtract 2 from -\frac{1}{4} to get -\frac{9}{4}.

$$\frac{5}{2}-\left(\frac{\frac{1}{2}}{-\frac{9}{4}}\right)^{-1}$$

Divide \frac{1}{2} by -\frac{9}{4} by multiplying \frac{1}{2} by the reciprocal of -\frac{9}{4}.

$$\frac{5}{2}-\left(\frac{1}{2}\left(-\frac{4}{9}\right)\right)^{-1}$$

Multiply \frac{1}{2} and -\frac{4}{9} to get -\frac{2}{9}.

$$\frac{5}{2}-\left(-\frac{2}{9}\right)^{-1}$$

Calculate -\frac{2}{9} to the power of -1 and get -\frac{9}{2}.

$$\frac{5}{2}-\left(-\frac{9}{2}\right)$$

The opposite of -\frac{9}{2} is \frac{9}{2}.

$$\frac{5}{2}+\frac{9}{2}$$

Add \frac{5}{2} and \frac{9}{2} to get 7.

$$7$$

Factor

$$7$$