Solve {l}{[(-2)^{3}+(-2)^{2}+(-2)^0-7]:(-5)}{[(-3)(-7)+(-5)(+2)-59]:(-12)}{[(-10)^2+(-10)^3]:(-10)^2-1}

$$\left. \begin{array} { l } { [ ( - 2 ) ^ { 3 } + ( - 2 ) ^ { 2 } + ( - 2 ) ^ { 0 } - 7 ] : ( - 5 ) } \\ { [ ( - 3 ) ( - 7 ) + ( - 5 ) ( + 2 ) - 59 ] : ( - 12 ) } \\ { [ ( - 10 ) ^ { 2 } + ( - 10 ) ^ { 3 } ] : ( - 10 ) ^ { 2 } - 1 } \end{array} \right.$$

Sort

$$-10,2,4$$

Solution Steps

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

$$sort(\frac{-8+\left(-2\right)^{2}+\left(-2\right)^{0}-7}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

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

$$sort(\frac{-8+4+\left(-2\right)^{0}-7}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Add -8 and 4 to get -4.

$$sort(\frac{-4+\left(-2\right)^{0}-7}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Calculate -2 to the power of 0 and get 1.

$$sort(\frac{-4+1-7}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Add -4 and 1 to get -3.

$$sort(\frac{-3-7}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Subtract 7 from -3 to get -10.

$$sort(\frac{-10}{-5},\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Divide -10 by -5 to get 2.

$$sort(2,\frac{-3\left(-7\right)-5\times 2-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Do the multiplications.

$$sort(2,\frac{21-10-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Subtract 10 from 21 to get 11.

$$sort(2,\frac{11-59}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Subtract 59 from 11 to get -48.

$$sort(2,\frac{-48}{-12},\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Divide -48 by -12 to get 4.

$$sort(2,4,\frac{\left(-10\right)^{2}+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Calculate -10 to the power of 2 and get 100.

$$sort(2,4,\frac{100+\left(-10\right)^{3}}{\left(-10\right)^{2}}-1)$$

Calculate -10 to the power of 3 and get -1000.

$$sort(2,4,\frac{100-1000}{\left(-10\right)^{2}}-1)$$

Subtract 1000 from 100 to get -900.

$$sort(2,4,\frac{-900}{\left(-10\right)^{2}}-1)$$

Calculate -10 to the power of 2 and get 100.

$$sort(2,4,\frac{-900}{100}-1)$$

Divide -900 by 100 to get -9.

$$sort(2,4,-9-1)$$

Subtract 1 from -9 to get -10.

$$sort(2,4,-10)$$

To sort the list, start from a single element 2.

$$2$$

Insert 4 to the appropriate location in the new list.

$$2,4$$

Insert -10 to the appropriate location in the new list.

$$-10,2,4$$

Evaluate

$$2,\ 4,\ -10$$