Solve frac{25^{6}*7^{9}*10^{9}*9^6}{3^4*5^2*99^1}

$$\frac { 25 ^ { 6 } \times 7 ^ { 9 } \times 10 ^ { 9 } \times 9 ^ { 6 } } { 3 ^ { 4 } \times 5 ^ { 2 } \times 99 ^ { 1 } }$$

Evaluate

$$\frac{287283002958984375000000000}{11}\approx 2.611663663 \cdot 10^{25}$$

Solution Steps

Calculate 25 to the power of 6 and get 244140625.

$$\frac{244140625\times 7^{9}\times 10^{9}\times 9^{6}}{3^{4}\times 5^{2}\times 99^{1}}$$

Calculate 7 to the power of 9 and get 40353607.

$$\frac{244140625\times 40353607\times 10^{9}\times 9^{6}}{3^{4}\times 5^{2}\times 99^{1}}$$

Multiply 244140625 and 40353607 to get 9851954833984375.

$$\frac{9851954833984375\times 10^{9}\times 9^{6}}{3^{4}\times 5^{2}\times 99^{1}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{9851954833984375\times 1000000000\times 9^{6}}{3^{4}\times 5^{2}\times 99^{1}}$$

Multiply 9851954833984375 and 1000000000 to get 9851954833984375000000000.

$$\frac{9851954833984375000000000\times 9^{6}}{3^{4}\times 5^{2}\times 99^{1}}$$

Calculate 9 to the power of 6 and get 531441.

$$\frac{9851954833984375000000000\times 531441}{3^{4}\times 5^{2}\times 99^{1}}$$

Multiply 9851954833984375000000000 and 531441 to get 5235732728927490234375000000000.

$$\frac{5235732728927490234375000000000}{3^{4}\times 5^{2}\times 99^{1}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{5235732728927490234375000000000}{81\times 5^{2}\times 99^{1}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{5235732728927490234375000000000}{81\times 25\times 99^{1}}$$

Multiply 81 and 25 to get 2025.

$$\frac{5235732728927490234375000000000}{2025\times 99^{1}}$$

Calculate 99 to the power of 1 and get 99.

$$\frac{5235732728927490234375000000000}{2025\times 99}$$

Multiply 2025 and 99 to get 200475.

$$\frac{5235732728927490234375000000000}{200475}$$

Reduce the fraction \frac{5235732728927490234375000000000}{200475} to lowest terms by extracting and canceling out 18225.

$$\frac{287283002958984375000000000}{11}$$

Factor

$$\frac{2 ^ {9} \cdot 3 ^ {6} \cdot 5 ^ {19} \cdot 7 ^ {9}}{11} = 2.611663663263494 \times 10^{25}$$