Solve sqrt[4]{8^4-6^4/6^4-2^4}

$$\sqrt[ 4 ] { \frac { 8 ^ { 4 } - 6 ^ { 4 } } { 6 ^ { 4 } - 2 ^ { 4 } } }$$

Evaluate

$$\frac{\sqrt[4]{35}}{2}\approx 1.21614964$$

Solution Steps

Calculate 8 to the power of 4 and get 4096.

$$\sqrt[4]{\frac{4096-6^{4}}{6^{4}-2^{4}}}$$

Calculate 6 to the power of 4 and get 1296.

$$\sqrt[4]{\frac{4096-1296}{6^{4}-2^{4}}}$$

Subtract 1296 from 4096 to get 2800.

$$\sqrt[4]{\frac{2800}{6^{4}-2^{4}}}$$

Calculate 6 to the power of 4 and get 1296.

$$\sqrt[4]{\frac{2800}{1296-2^{4}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt[4]{\frac{2800}{1296-16}}$$

Subtract 16 from 1296 to get 1280.

$$\sqrt[4]{\frac{2800}{1280}}$$

Reduce the fraction \frac{2800}{1280} to lowest terms by extracting and canceling out 80.

$$\sqrt[4]{\frac{35}{16}}$$