Solve (1/2)^2+[-(-7)+(-1)^3]*2/3

$$( \frac { 1 } { 2 } ) ^ { 2 } + [ - ( - 7 ) + ( - 1 ) ^ { 3 } ] \times \frac { 2 } { 3 }$$

Evaluate

$$\frac{17}{4}=4.25$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

The opposite of -7 is 7.

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

Calculate -1 to the power of 3 and get -1.

$$\frac{1}{4}+\left(7-1\right)\times \frac{2}{3}$$

Subtract 1 from 7 to get 6.

$$\frac{1}{4}+6\times \frac{2}{3}$$

Express 6\times \frac{2}{3} as a single fraction.

$$\frac{1}{4}+\frac{6\times 2}{3}$$

Multiply 6 and 2 to get 12.

$$\frac{1}{4}+\frac{12}{3}$$

Divide 12 by 3 to get 4.

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

Convert 4 to fraction \frac{16}{4}.

$$\frac{1}{4}+\frac{16}{4}$$

Since \frac{1}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+16}{4}$$

Add 1 and 16 to get 17.

$$\frac{17}{4}$$

Factor

$$\frac{17}{2 ^ {2}} = 4\frac{1}{4} = 4.25$$