Solve 2^{3}+(-2)^{4}-(-2)^{5}+(-3)^2+(sqrt{3})^2-(2sqrt{2})^2-2^2

$$2 ^ { 3 } + ( - 2 ) ^ { 4 } - ( - 2 ) ^ { 5 } + ( - 3 ) ^ { 2 } + ( \sqrt { 3 } ) ^ { 2 } - ( 2 \sqrt { 2 } ) ^ { 2 } - 2 ^ { 2 }$$

Evaluate

$$56$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8+\left(-2\right)^{4}-\left(-2\right)^{5}+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Calculate -2 to the power of 4 and get 16.

$$8+16-\left(-2\right)^{5}+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Add 8 and 16 to get 24.

$$24-\left(-2\right)^{5}+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Calculate -2 to the power of 5 and get -32.

$$24-\left(-32\right)+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

The opposite of -32 is 32.

$$24+32+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Add 24 and 32 to get 56.

$$56+\left(-3\right)^{2}+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Calculate -3 to the power of 2 and get 9.

$$56+9+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Add 56 and 9 to get 65.

$$65+\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}-2^{2}$$

The square of \sqrt{3} is 3.

$$65+3-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Add 65 and 3 to get 68.

$$68-\left(2\sqrt{2}\right)^{2}-2^{2}$$

Expand \left(2\sqrt{2}\right)^{2}.

$$68-2^{2}\left(\sqrt{2}\right)^{2}-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$68-4\left(\sqrt{2}\right)^{2}-2^{2}$$

The square of \sqrt{2} is 2.

$$68-4\times 2-2^{2}$$

Multiply 4 and 2 to get 8.

$$68-8-2^{2}$$

Subtract 8 from 68 to get 60.

$$60-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$60-4$$

Subtract 4 from 60 to get 56.

$$56$$

Factor

$$2^{3}\times 7$$