Solve -1^4div5^2*(-6/3)+|0.87/4-1|

$$- 1 ^ { 4 } \div 5 ^ { 2 } \times ( - \frac { 6 } { 3 } ) + | 0.8 \frac { 7 } { 4 } - 1 |$$

Evaluate

$$1.63$$

Solution Steps

Calculate 1 to the power of 4 and get 1.

$$\frac{-1}{5^{2}}\left(-\frac{6}{3}\right)+|\frac{0.8\times 4+7}{4}-1|$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-1}{25}\left(-\frac{6}{3}\right)+|\frac{0.8\times 4+7}{4}-1|$$

Fraction \frac{-1}{25} can be rewritten as -\frac{1}{25} by extracting the negative sign.

$$-\frac{1}{25}\left(-\frac{6}{3}\right)+|\frac{0.8\times 4+7}{4}-1|$$

Divide 6 by 3 to get 2.

$$-\frac{1}{25}\left(-2\right)+|\frac{0.8\times 4+7}{4}-1|$$

Express -\frac{1}{25}\left(-2\right) as a single fraction.

$$\frac{-\left(-2\right)}{25}+|\frac{0.8\times 4+7}{4}-1|$$

Multiply -1 and -2 to get 2.

$$\frac{2}{25}+|\frac{0.8\times 4+7}{4}-1|$$

Multiply 0.8 and 4 to get 3.2.

$$\frac{2}{25}+|\frac{3.2+7}{4}-1|$$

Add 3.2 and 7 to get 10.2.

$$\frac{2}{25}+|\frac{10.2}{4}-1|$$

Expand \frac{10.2}{4} by multiplying both numerator and the denominator by 10.

$$\frac{2}{25}+|\frac{102}{40}-1|$$

Reduce the fraction \frac{102}{40} to lowest terms by extracting and canceling out 2.

$$\frac{2}{25}+|\frac{51}{20}-1|$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{2}{25}+|\frac{51}{20}-\frac{20}{20}|$$

Since \frac{51}{20} and \frac{20}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{25}+|\frac{51-20}{20}|$$

Subtract 20 from 51 to get 31.

$$\frac{2}{25}+|\frac{31}{20}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{31}{20} is \frac{31}{20}.

$$\frac{2}{25}+\frac{31}{20}$$

Least common multiple of 25 and 20 is 100. Convert \frac{2}{25} and \frac{31}{20} to fractions with denominator 100.

$$\frac{8}{100}+\frac{155}{100}$$

Since \frac{8}{100} and \frac{155}{100} have the same denominator, add them by adding their numerators.

$$\frac{8+155}{100}$$

Add 8 and 155 to get 163.

$$\frac{163}{100}$$

Factor

$$\frac{163}{2 ^ {2} \cdot 5 ^ {2}} = 1\frac{63}{100} = 1.63$$