Solve [(7-(3-8))-3]^2/2[(16div2^2)-(4*4)]

$$\frac { [ ( 7 - ( 3 - 8 ) ) - 3 ] ^ { 2 } } { 2 [ ( 16 \div 2 ^ { 2 } ) - ( 4 \times 4 ) ] }$$

Evaluate

$$-\frac{27}{8}=-3.375$$

Solution Steps

Subtract 8 from 3 to get -5.

$$\frac{\left(7-\left(-5\right)-3\right)^{2}}{2\left(\frac{16}{2^{2}}-4\times 4\right)}$$

The opposite of -5 is 5.

$$\frac{\left(7+5-3\right)^{2}}{2\left(\frac{16}{2^{2}}-4\times 4\right)}$$

Add 7 and 5 to get 12.

$$\frac{\left(12-3\right)^{2}}{2\left(\frac{16}{2^{2}}-4\times 4\right)}$$

Subtract 3 from 12 to get 9.

$$\frac{9^{2}}{2\left(\frac{16}{2^{2}}-4\times 4\right)}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{81}{2\left(\frac{16}{2^{2}}-4\times 4\right)}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81}{2\left(\frac{16}{4}-4\times 4\right)}$$

Divide 16 by 4 to get 4.

$$\frac{81}{2\left(4-4\times 4\right)}$$

Multiply 4 and 4 to get 16.

$$\frac{81}{2\left(4-16\right)}$$

Subtract 16 from 4 to get -12.

$$\frac{81}{2\left(-12\right)}$$

Multiply 2 and -12 to get -24.

$$\frac{81}{-24}$$

Reduce the fraction \frac{81}{-24} to lowest terms by extracting and canceling out 3.

$$-\frac{27}{8}$$

Factor

$$-\frac{27}{8} = -3\frac{3}{8} = -3.375$$