Solve 1^4+1/6*[|-2|-(-3)^3-(-2)^2]div(-5/2)^2

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Calculate 1 to the power of 4 and get 1.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

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

Calculate -3 to the power of 3 and get -27.

$$1+\frac{\frac{1}{6}\left(2-\left(-27\right)-\left(-2\right)^{2}\right)}{\left(-\frac{5}{2}\right)^{2}}$$

The opposite of -27 is 27.

$$1+\frac{\frac{1}{6}\left(2+27-\left(-2\right)^{2}\right)}{\left(-\frac{5}{2}\right)^{2}}$$

Add 2 and 27 to get 29.

$$1+\frac{\frac{1}{6}\left(29-\left(-2\right)^{2}\right)}{\left(-\frac{5}{2}\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$1+\frac{\frac{1}{6}\left(29-4\right)}{\left(-\frac{5}{2}\right)^{2}}$$

Subtract 4 from 29 to get 25.

$$1+\frac{\frac{1}{6}\times 25}{\left(-\frac{5}{2}\right)^{2}}$$

Multiply \frac{1}{6} and 25 to get \frac{25}{6}.

$$1+\frac{\frac{25}{6}}{\left(-\frac{5}{2}\right)^{2}}$$

Calculate -\frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$1+\frac{\frac{25}{6}}{\frac{25}{4}}$$

Divide \frac{25}{6} by \frac{25}{4} by multiplying \frac{25}{6} by the reciprocal of \frac{25}{4}.

$$1+\frac{25}{6}\times \frac{4}{25}$$

Multiply \frac{25}{6} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{25\times 4}{6\times 25}$$

Cancel out 25 in both numerator and denominator.

$$1+\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$1+\frac{2}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}+\frac{2}{3}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{3}$$

Add 3 and 2 to get 5.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$