Solve (97^3+83^5/180-97*83):(35^2-28^2)=

$$( \frac { 97 ^ { 3 } + 83 ^ { 5 } } { 180 } - 97 \cdot 83 ) : ( 35 ^ { 2 } - 28 ^ { 2 } ) =$$

Evaluate

$$\frac{46886954}{945}\approx 49615.824338624$$

Solution Steps

Calculate 97 to the power of 3 and get 912673.

$$\frac{\frac{912673+83^{5}}{180}-97\times 83}{35^{2}-28^{2}}$$

Calculate 83 to the power of 5 and get 3939040643.

$$\frac{\frac{912673+3939040643}{180}-97\times 83}{35^{2}-28^{2}}$$

Add 912673 and 3939040643 to get 3939953316.

$$\frac{\frac{3939953316}{180}-97\times 83}{35^{2}-28^{2}}$$

Reduce the fraction \frac{3939953316}{180} to lowest terms by extracting and canceling out 12.

$$\frac{\frac{328329443}{15}-97\times 83}{35^{2}-28^{2}}$$

Multiply 97 and 83 to get 8051.

$$\frac{\frac{328329443}{15}-8051}{35^{2}-28^{2}}$$

Convert 8051 to fraction \frac{120765}{15}.

$$\frac{\frac{328329443}{15}-\frac{120765}{15}}{35^{2}-28^{2}}$$

Since \frac{328329443}{15} and \frac{120765}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{328329443-120765}{15}}{35^{2}-28^{2}}$$

Subtract 120765 from 328329443 to get 328208678.

$$\frac{\frac{328208678}{15}}{35^{2}-28^{2}}$$

Calculate 35 to the power of 2 and get 1225.

$$\frac{\frac{328208678}{15}}{1225-28^{2}}$$

Calculate 28 to the power of 2 and get 784.

$$\frac{\frac{328208678}{15}}{1225-784}$$

Subtract 784 from 1225 to get 441.

$$\frac{\frac{328208678}{15}}{441}$$

Express \frac{\frac{328208678}{15}}{441} as a single fraction.

$$\frac{328208678}{15\times 441}$$

Multiply 15 and 441 to get 6615.

$$\frac{328208678}{6615}$$

Reduce the fraction \frac{328208678}{6615} to lowest terms by extracting and canceling out 7.

$$\frac{46886954}{945}$$

Factor

$$\frac{2 \cdot 1637 \cdot 14321}{3 ^ {3} \cdot 5 \cdot 7} = 49615\frac{779}{945} = 49615.82433862434$$