Solve 43^3left(83^2-5right)-3^4-4(2(3))/{left(3^2-5right)^2}

$$\frac{ 4 { 3 }^{ 3 } \left( { 83 }^{ 2 } -5 \right) - { 3 }^{ 4 } -4(2(3)) }{ { \left( { 3 }^{ 2 } -5 \right) }^{ 2 } }$$

Evaluate

$$\frac{743367}{16}=46460.4375$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{4\times 27\left(83^{2}-5\right)-3^{4}-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Multiply 4 and 27 to get 108.

$$\frac{108\left(83^{2}-5\right)-3^{4}-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Calculate 83 to the power of 2 and get 6889.

$$\frac{108\left(6889-5\right)-3^{4}-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Subtract 5 from 6889 to get 6884.

$$\frac{108\times 6884-3^{4}-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Multiply 108 and 6884 to get 743472.

$$\frac{743472-3^{4}-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{743472-81-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Subtract 81 from 743472 to get 743391.

$$\frac{743391-4\times 2\times 3}{\left(3^{2}-5\right)^{2}}$$

Multiply 4 and 2 to get 8.

$$\frac{743391-8\times 3}{\left(3^{2}-5\right)^{2}}$$

Multiply 8 and 3 to get 24.

$$\frac{743391-24}{\left(3^{2}-5\right)^{2}}$$

Subtract 24 from 743391 to get 743367.

$$\frac{743367}{\left(3^{2}-5\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{743367}{\left(9-5\right)^{2}}$$

Subtract 5 from 9 to get 4.

$$\frac{743367}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{743367}{16}$$

Factor

$$\frac{3 \cdot 37 ^ {2} \cdot 181}{2 ^ {4}} = 46460\frac{7}{16} = 46460.4375$$