Solve frac{sqrt{9^{6}*12^{12}*sqrt{5^{16}*3^{4}}}}{sqrt{9^6*12^10*5^6*3^4}}

$$\frac { \sqrt { 9 ^ { 6 } \times 12 ^ { 12 } \times \sqrt { 5 ^ { 16 } \times 3 ^ { 4 } } } } { \sqrt { 9 ^ { 6 } \times 12 ^ { 10 } \times 5 ^ { 6 } \times 3 ^ { 4 } } }$$

Evaluate

$$20$$

Solution Steps

Calculate 9 to the power of 6 and get 531441.

$$\frac{\sqrt{531441\times 12^{12}\sqrt{5^{16}\times 3^{4}}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate 12 to the power of 12 and get 8916100448256.

$$\frac{\sqrt{531441\times 8916100448256\sqrt{5^{16}\times 3^{4}}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Multiply 531441 and 8916100448256 to get 4738381338321616896.

$$\frac{\sqrt{4738381338321616896\sqrt{5^{16}\times 3^{4}}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate 5 to the power of 16 and get 152587890625.

$$\frac{\sqrt{4738381338321616896\sqrt{152587890625\times 3^{4}}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\sqrt{4738381338321616896\sqrt{152587890625\times 81}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Multiply 152587890625 and 81 to get 12359619140625.

$$\frac{\sqrt{4738381338321616896\sqrt{12359619140625}}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate the square root of 12359619140625 and get 3515625.

$$\frac{\sqrt{4738381338321616896\times 3515625}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Multiply 4738381338321616896 and 3515625 to get 16658371892536934400000000.

$$\frac{\sqrt{16658371892536934400000000}}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate the square root of 16658371892536934400000000 and get 4081466880000.

$$\frac{4081466880000}{\sqrt{9^{6}\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate 9 to the power of 6 and get 531441.

$$\frac{4081466880000}{\sqrt{531441\times 12^{10}\times 5^{6}\times 3^{4}}}$$

Calculate 12 to the power of 10 and get 61917364224.

$$\frac{4081466880000}{\sqrt{531441\times 61917364224\times 5^{6}\times 3^{4}}}$$

Multiply 531441 and 61917364224 to get 32905425960566784.

$$\frac{4081466880000}{\sqrt{32905425960566784\times 5^{6}\times 3^{4}}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{4081466880000}{\sqrt{32905425960566784\times 15625\times 3^{4}}}$$

Multiply 32905425960566784 and 15625 to get 514147280633856000000.

$$\frac{4081466880000}{\sqrt{514147280633856000000\times 3^{4}}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{4081466880000}{\sqrt{514147280633856000000\times 81}}$$

Multiply 514147280633856000000 and 81 to get 41645929731342336000000.

$$\frac{4081466880000}{\sqrt{41645929731342336000000}}$$

Calculate the square root of 41645929731342336000000 and get 204073344000.

$$\frac{4081466880000}{204073344000}$$

Divide 4081466880000 by 204073344000 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$