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

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

Evaluate

$$4081466880000$$

Solution Steps

Calculate 9 to the power of 6 and get 531441.

$$\sqrt{531441\times 12^{12}\sqrt{5^{16}\times 3^{4}}}$$

Calculate 12 to the power of 12 and get 8916100448256.

$$\sqrt{531441\times 8916100448256\sqrt{5^{16}\times 3^{4}}}$$

Multiply 531441 and 8916100448256 to get 4738381338321616896.

$$\sqrt{4738381338321616896\sqrt{5^{16}\times 3^{4}}}$$

Calculate 5 to the power of 16 and get 152587890625.

$$\sqrt{4738381338321616896\sqrt{152587890625\times 3^{4}}}$$

Calculate 3 to the power of 4 and get 81.

$$\sqrt{4738381338321616896\sqrt{152587890625\times 81}}$$

Multiply 152587890625 and 81 to get 12359619140625.

$$\sqrt{4738381338321616896\sqrt{12359619140625}}$$

Calculate the square root of 12359619140625 and get 3515625.

$$\sqrt{4738381338321616896\times 3515625}$$

Multiply 4738381338321616896 and 3515625 to get 16658371892536934400000000.

$$\sqrt{16658371892536934400000000}$$

Calculate the square root of 16658371892536934400000000 and get 4081466880000.

$$4081466880000$$

Factor

$$2^{12}\times 3^{13}\times 5^{4}$$