Solve 101/10+10^-3-(1/10)^-1-10^-3-4/frac{4{5}(-11/5)^-1}

$$10 \frac { 1 } { 10 } + 10 ^ { - 3 } - ( \frac { 1 } { 10 } ) ^ { - 1 } - 10 ^ { - 3 } - \frac { 4 } { \frac { 4 } { 5 } ( - 1 \frac { 1 } { 5 } ) ^ { - 1 } }$$

Evaluate

$$\frac{61}{10}=6.1$$

Solution Steps

Multiply 10 and 10 to get 100.

$$\frac{100+1}{10}+10^{-3}-\left(\frac{1}{10}\right)^{-1}-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Add 100 and 1 to get 101.

$$\frac{101}{10}+10^{-3}-\left(\frac{1}{10}\right)^{-1}-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{101}{10}+\frac{1}{1000}-\left(\frac{1}{10}\right)^{-1}-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Add \frac{101}{10} and \frac{1}{1000} to get \frac{10101}{1000}.

$$\frac{10101}{1000}-\left(\frac{1}{10}\right)^{-1}-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Calculate \frac{1}{10} to the power of -1 and get 10.

$$\frac{10101}{1000}-10-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Subtract 10 from \frac{10101}{1000} to get \frac{101}{1000}.

$$\frac{101}{1000}-10^{-3}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{101}{1000}-\frac{1}{1000}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Subtract \frac{1}{1000} from \frac{101}{1000} to get \frac{1}{10}.

$$\frac{1}{10}-\frac{4}{\frac{4}{5}\left(-\frac{1\times 5+1}{5}\right)^{-1}}$$

Multiply 1 and 5 to get 5.

$$\frac{1}{10}-\frac{4}{\frac{4}{5}\left(-\frac{5+1}{5}\right)^{-1}}$$

Add 5 and 1 to get 6.

$$\frac{1}{10}-\frac{4}{\frac{4}{5}\left(-\frac{6}{5}\right)^{-1}}$$

Calculate -\frac{6}{5} to the power of -1 and get -\frac{5}{6}.

$$\frac{1}{10}-\frac{4}{\frac{4}{5}\left(-\frac{5}{6}\right)}$$

Multiply \frac{4}{5} and -\frac{5}{6} to get -\frac{2}{3}.

$$\frac{1}{10}-\frac{4}{-\frac{2}{3}}$$

Divide 4 by -\frac{2}{3} by multiplying 4 by the reciprocal of -\frac{2}{3}.

$$\frac{1}{10}-4\left(-\frac{3}{2}\right)$$

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

$$\frac{1}{10}-\left(-6\right)$$

The opposite of -6 is 6.

$$\frac{1}{10}+6$$

Add \frac{1}{10} and 6 to get \frac{61}{10}.

$$\frac{61}{10}$$

Factor

$$\frac{61}{2 \cdot 5} = 6\frac{1}{10} = 6.1$$