Solve 2^2(-2)+2-(8-7-3)^3+2div(-4-3-2)^3

$$2 ^ { 2 } ( - 2 ) + 2 - ( 8 - 7 - 3 ) ^ { 3 } + 2 \div ( - 4 - 3 - 2 ) ^ { 3 }$$

Evaluate

$$\frac{1456}{729}\approx 1.997256516$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4\left(-2\right)+2-\left(8-7-3\right)^{3}+\frac{2}{\left(-4-3-2\right)^{3}}$$

Multiply 4 and -2 to get -8.

$$-8+2-\left(8-7-3\right)^{3}+\frac{2}{\left(-4-3-2\right)^{3}}$$

Add -8 and 2 to get -6.

$$-6-\left(8-7-3\right)^{3}+\frac{2}{\left(-4-3-2\right)^{3}}$$

Subtract 7 from 8 to get 1.

$$-6-\left(1-3\right)^{3}+\frac{2}{\left(-4-3-2\right)^{3}}$$

Subtract 3 from 1 to get -2.

$$-6-\left(-2\right)^{3}+\frac{2}{\left(-4-3-2\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$-6-\left(-8\right)+\frac{2}{\left(-4-3-2\right)^{3}}$$

The opposite of -8 is 8.

$$-6+8+\frac{2}{\left(-4-3-2\right)^{3}}$$

Add -6 and 8 to get 2.

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

Subtract 3 from -4 to get -7.

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

Subtract 2 from -7 to get -9.

$$2+\frac{2}{\left(-9\right)^{3}}$$

Calculate -9 to the power of 3 and get -729.

$$2+\frac{2}{-729}$$

Fraction \frac{2}{-729} can be rewritten as -\frac{2}{729} by extracting the negative sign.

$$2-\frac{2}{729}$$

Subtract \frac{2}{729} from 2 to get \frac{1456}{729}.

$$\frac{1456}{729}$$

Factor

$$\frac{2 ^ {4} \cdot 7 \cdot 13}{3 ^ {6}} = 1\frac{727}{729} = 1.9972565157750344$$