Solve frac{4(3)^{3}(83^2-5)-(3^4-4)*(28)}{(3^2-5)^2}

$$\frac { 4 ( 3 ) ^ { 3 } ( 83 ^ { 2 } - 5 ) - ( 3 ^ { 4 } - 4 ) \cdot ( 28 ) } { ( 3 ^ { 2 } - 5 ) ^ { 2 } }$$

Evaluate

$$\frac{185329}{4}=46332.25$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{4\times 27\left(83^{2}-5\right)-\left(3^{4}-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Multiply 4 and 27 to get 108.

$$\frac{108\left(83^{2}-5\right)-\left(3^{4}-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Calculate 83 to the power of 2 and get 6889.

$$\frac{108\left(6889-5\right)-\left(3^{4}-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Subtract 5 from 6889 to get 6884.

$$\frac{108\times 6884-\left(3^{4}-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Multiply 108 and 6884 to get 743472.

$$\frac{743472-\left(3^{4}-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{743472-\left(81-4\right)\times 28}{\left(3^{2}-5\right)^{2}}$$

Subtract 4 from 81 to get 77.

$$\frac{743472-77\times 28}{\left(3^{2}-5\right)^{2}}$$

Multiply 77 and 28 to get 2156.

$$\frac{743472-2156}{\left(3^{2}-5\right)^{2}}$$

Subtract 2156 from 743472 to get 741316.

$$\frac{741316}{\left(3^{2}-5\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{741316}{\left(9-5\right)^{2}}$$

Subtract 5 from 9 to get 4.

$$\frac{741316}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{741316}{16}$$

Reduce the fraction \frac{741316}{16} to lowest terms by extracting and canceling out 4.

$$\frac{185329}{4}$$

Factor

$$\frac{241 \cdot 769}{2 ^ {2}} = 46332\frac{1}{4} = 46332.25$$