Solve 2*(-2/3)^3-13*(-2/3)^2-5*(-2/3)+7

$$2 \times ( \frac { - 2 } { 3 } ) ^ { 3 } - 13 \times ( \frac { - 2 } { 3 } ) ^ { 2 } - 5 \times ( \frac { - 2 } { 3 } ) + 7$$

Evaluate

$$\frac{107}{27}\approx 3.962962963$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$2\left(-\frac{2}{3}\right)^{3}-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$2\left(-\frac{8}{27}\right)-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Multiply 2 and -\frac{8}{27} to get -\frac{16}{27}.

$$-\frac{16}{27}-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{16}{27}-13\left(-\frac{2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-\frac{16}{27}-13\times \frac{4}{9}-5\times \frac{-2}{3}+7$$

Multiply 13 and \frac{4}{9} to get \frac{52}{9}.

$$-\frac{16}{27}-\frac{52}{9}-5\times \frac{-2}{3}+7$$

Subtract \frac{52}{9} from -\frac{16}{27} to get -\frac{172}{27}.

$$-\frac{172}{27}-5\times \frac{-2}{3}+7$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{172}{27}-5\left(-\frac{2}{3}\right)+7$$

Multiply 5 and -\frac{2}{3} to get -\frac{10}{3}.

$$-\frac{172}{27}-\left(-\frac{10}{3}\right)+7$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$-\frac{172}{27}+\frac{10}{3}+7$$

Add -\frac{172}{27} and \frac{10}{3} to get -\frac{82}{27}.

$$-\frac{82}{27}+7$$

Add -\frac{82}{27} and 7 to get \frac{107}{27}.

$$\frac{107}{27}$$

Factor

$$\frac{107}{3 ^ {3}} = 3\frac{26}{27} = 3.962962962962963$$