Solve 3^3+{(-2)^3+[sqrt{16}(8div4-1)-(4-5)^2]}

$$3 ^ { 3 } + \{ ( - 2 ) ^ { 3 } + [ \sqrt { 16 } ( 8 \div 4 - 1 ) - ( 4 - 5 ) ^ { 2 } ] \}$$

Evaluate

$$22$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$27+\left(-2\right)^{3}+\sqrt{16}\left(\frac{8}{4}-1\right)-\left(4-5\right)^{2}$$

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

$$27-8+\sqrt{16}\left(\frac{8}{4}-1\right)-\left(4-5\right)^{2}$$

Subtract 8 from 27 to get 19.

$$19+\sqrt{16}\left(\frac{8}{4}-1\right)-\left(4-5\right)^{2}$$

Calculate the square root of 16 and get 4.

$$19+4\left(\frac{8}{4}-1\right)-\left(4-5\right)^{2}$$

Divide 8 by 4 to get 2.

$$19+4\left(2-1\right)-\left(4-5\right)^{2}$$

Subtract 1 from 2 to get 1.

$$19+4\times 1-\left(4-5\right)^{2}$$

Multiply 4 and 1 to get 4.

$$19+4-\left(4-5\right)^{2}$$

Subtract 5 from 4 to get -1.

$$19+4-\left(-1\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$19+4-1$$

Subtract 1 from 4 to get 3.

$$19+3$$

Add 19 and 3 to get 22.

$$22$$

Factor

$$2\times 11$$