Solve (36+32+16+16)(36*16-32*16)^2/(36+32)(36+16)(32+16)(32+16)=

$$\frac { ( 36 + 32 + 16 + 16 ) ( 36 \times 16 - 32 \times 16 ) ^ { 2 } } { ( 36 + 32 ) ( 36 + 16 ) ( 32 + 16 ) ( 32 + 16 ) } =$$

Evaluate

$$\frac{100}{1989}\approx 0.050276521$$

Solution Steps

Multiply 32+16 and 32+16 to get \left(32+16\right)^{2}.

$$\frac{\left(36+32+16+16\right)\left(36\times 16-32\times 16\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Add 36 and 32 to get 68.

$$\frac{\left(68+16+16\right)\left(36\times 16-32\times 16\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Add 68 and 16 to get 84.

$$\frac{\left(84+16\right)\left(36\times 16-32\times 16\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Add 84 and 16 to get 100.

$$\frac{100\left(36\times 16-32\times 16\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Multiply 36 and 16 to get 576.

$$\frac{100\left(576-32\times 16\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Multiply 32 and 16 to get 512.

$$\frac{100\left(576-512\right)^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Subtract 512 from 576 to get 64.

$$\frac{100\times 64^{2}}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Calculate 64 to the power of 2 and get 4096.

$$\frac{100\times 4096}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Multiply 100 and 4096 to get 409600.

$$\frac{409600}{\left(36+32\right)\left(36+16\right)\left(32+16\right)^{2}}$$

Add 36 and 32 to get 68.

$$\frac{409600}{68\left(36+16\right)\left(32+16\right)^{2}}$$

Add 36 and 16 to get 52.

$$\frac{409600}{68\times 52\left(32+16\right)^{2}}$$

Multiply 68 and 52 to get 3536.

$$\frac{409600}{3536\left(32+16\right)^{2}}$$

Add 32 and 16 to get 48.

$$\frac{409600}{3536\times 48^{2}}$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{409600}{3536\times 2304}$$

Multiply 3536 and 2304 to get 8146944.

$$\frac{409600}{8146944}$$

Reduce the fraction \frac{409600}{8146944} to lowest terms by extracting and canceling out 4096.

$$\frac{100}{1989}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2} \cdot 13 \cdot 17} = 0.05027652086475616$$