Solve frac{2^{3}*5^{2}*49^3*3^5}{6^3*100}*(35)^2

$$\frac { 2 ^ { 3 } \cdot 5 ^ { 2 } \cdot 49 ^ { 3 } \cdot 3 ^ { 5 } } { 6 ^ { 3 } \cdot 100 } \cdot ( 35 ) ^ { 2 }$$

Evaluate

$$\frac{1297080225}{4}=324270056.25$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\frac{8\times 5^{2}\times 49^{3}\times 3^{5}}{6^{3}\times 100}\times 35^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{8\times 25\times 49^{3}\times 3^{5}}{6^{3}\times 100}\times 35^{2}$$

Multiply 8 and 25 to get 200.

$$\frac{200\times 49^{3}\times 3^{5}}{6^{3}\times 100}\times 35^{2}$$

Calculate 49 to the power of 3 and get 117649.

$$\frac{200\times 117649\times 3^{5}}{6^{3}\times 100}\times 35^{2}$$

Multiply 200 and 117649 to get 23529800.

$$\frac{23529800\times 3^{5}}{6^{3}\times 100}\times 35^{2}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{23529800\times 243}{6^{3}\times 100}\times 35^{2}$$

Multiply 23529800 and 243 to get 5717741400.

$$\frac{5717741400}{6^{3}\times 100}\times 35^{2}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{5717741400}{216\times 100}\times 35^{2}$$

Multiply 216 and 100 to get 21600.

$$\frac{5717741400}{21600}\times 35^{2}$$

Reduce the fraction \frac{5717741400}{21600} to lowest terms by extracting and canceling out 5400.

$$\frac{1058841}{4}\times 35^{2}$$

Calculate 35 to the power of 2 and get 1225.

$$\frac{1058841}{4}\times 1225$$

Express \frac{1058841}{4}\times 1225 as a single fraction.

$$\frac{1058841\times 1225}{4}$$

Multiply 1058841 and 1225 to get 1297080225.

$$\frac{1297080225}{4}$$

Factor

$$\frac{3 ^ {2} \cdot 5 ^ {2} \cdot 7 ^ {8}}{2 ^ {2}} = 324270056\frac{1}{4} = 324270056.25$$