Solve S-{7*sqrt{16}:2^2-[-2^1*(7-3)+6]:2}

$$S - \{ 7 \times \sqrt { 16 } : 2 ^ { 2 } - [ - 2 ^ { 1 } \times ( 7 - 3 ) + 6 ] : 2 \}$$

Evaluate

$$S-8$$

Solution Steps

Calculate the square root of 16 and get 4.

$$S-\left(\frac{7\times 4}{2^{2}}-\frac{\left(-2^{1}\right)\left(7-3\right)+6}{2}\right)$$

Multiply 7 and 4 to get 28.

$$S-\left(\frac{28}{2^{2}}-\frac{\left(-2^{1}\right)\left(7-3\right)+6}{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$S-\left(\frac{28}{4}-\frac{\left(-2^{1}\right)\left(7-3\right)+6}{2}\right)$$

Divide 28 by 4 to get 7.

$$S-\left(7-\frac{\left(-2^{1}\right)\left(7-3\right)+6}{2}\right)$$

Calculate 2 to the power of 1 and get 2.

$$S-\left(7-\frac{-2\left(7-3\right)+6}{2}\right)$$

Subtract 3 from 7 to get 4.

$$S-\left(7-\frac{-2\times 4+6}{2}\right)$$

Multiply -2 and 4 to get -8.

$$S-\left(7-\frac{-8+6}{2}\right)$$

Add -8 and 6 to get -2.

$$S-\left(7-\frac{-2}{2}\right)$$

Divide -2 by 2 to get -1.

$$S-\left(7-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$S-\left(7+1\right)$$

Add 7 and 1 to get 8.

$$S-8$$

Factor

$$S-8$$