Solve sqrt[10]{16^10}*sqrt[4]{8^12}*sqrt[5]{16^10}

$$\sqrt[ 10 ] { 16 ^ { 10 } } \cdot \sqrt[ 4 ] { 8 ^ { 12 } } \cdot \sqrt[ 5 ] { 16 ^ { 10 } }$$

Evaluate

$$2097152$$

Solution Steps

Calculate 16 to the power of 10 and get 1099511627776.

$$\sqrt[10]{1099511627776}\sqrt[4]{8^{12}}\sqrt[5]{16^{10}}$$

Calculate \sqrt[10]{1099511627776} and get 16.

$$16\sqrt[4]{8^{12}}\sqrt[5]{16^{10}}$$

Calculate 8 to the power of 12 and get 68719476736.

$$16\sqrt[4]{68719476736}\sqrt[5]{16^{10}}$$

Calculate \sqrt[4]{68719476736} and get 512.

$$16\times 512\sqrt[5]{16^{10}}$$

Multiply 16 and 512 to get 8192.

$$8192\sqrt[5]{16^{10}}$$

Calculate 16 to the power of 10 and get 1099511627776.

$$8192\sqrt[5]{1099511627776}$$

Calculate \sqrt[5]{1099511627776} and get 256.

$$8192\times 256$$

Multiply 8192 and 256 to get 2097152.

$$2097152$$

Factor

$$2^{21}$$