Solve sqrt[6]{3^8*5^4*7^6}

$$\sqrt[ 6 ] { 3 ^ { 8 } \cdot 5 ^ { 4 } \cdot 7 ^ { 6 } }$$

Evaluate

$$21\sqrt[3]{75}\approx 88.560429857$$

Solution Steps

Calculate 3 to the power of 8 and get 6561.

$$\sqrt[6]{6561\times 5^{4}\times 7^{6}}$$

Calculate 5 to the power of 4 and get 625.

$$\sqrt[6]{6561\times 625\times 7^{6}}$$

Multiply 6561 and 625 to get 4100625.

$$\sqrt[6]{4100625\times 7^{6}}$$

Calculate 7 to the power of 6 and get 117649.

$$\sqrt[6]{4100625\times 117649}$$

Multiply 4100625 and 117649 to get 482434430625.

$$\sqrt[6]{482434430625}$$