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

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

Evaluate

$$\frac{50}{663}\approx 0.075414781$$

Solution Steps

Add 36 and 32 to get 68.

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

Add 68 and 16 to get 84.

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

Add 84 and 16 to get 100.

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

Multiply 36 and 16 to get 576.

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

Multiply 32 and 16 to get 512.

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

Subtract 512 from 576 to get 64.

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

Calculate 64 to the power of 2 and get 4096.

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

Multiply 100 and 4096 to get 409600.

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

Add 36 and 32 to get 68.

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

Add 36 and 16 to get 52.

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

Multiply 68 and 52 to get 3536.

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

Add 32 and 16 to get 48.

$$\frac{409600}{3536\times 48\left(16+16\right)}$$

Multiply 3536 and 48 to get 169728.

$$\frac{409600}{169728\left(16+16\right)}$$

Add 16 and 16 to get 32.

$$\frac{409600}{169728\times 32}$$

Multiply 169728 and 32 to get 5431296.

$$\frac{409600}{5431296}$$

Reduce the fraction \frac{409600}{5431296} to lowest terms by extracting and canceling out 8192.

$$\frac{50}{663}$$

Factor

$$\frac{2 \cdot 5 ^ {2}}{3 \cdot 13 \cdot 17} = 0.07541478129713423$$