Solve 8^4/11^46sqrt{36+12+2}

$$\frac{ { 8 }^{ 4 } }{ { 11 }^{ 4 } } 6 \sqrt{ 36+12+2 }$$

Evaluate

$$\frac{122880\sqrt{2}}{14641}\approx 11.869309647$$

Solution Steps

Calculate 8 to the power of 4 and get 4096.

$$6\times \frac{4096}{11^{4}}\sqrt{36+12+2}$$

Calculate 11 to the power of 4 and get 14641.

$$6\times \frac{4096}{14641}\sqrt{36+12+2}$$

Express 6\times \frac{4096}{14641} as a single fraction.

$$\frac{6\times 4096}{14641}\sqrt{36+12+2}$$

Multiply 6 and 4096 to get 24576.

$$\frac{24576}{14641}\sqrt{36+12+2}$$

Add 36 and 12 to get 48.

$$\frac{24576}{14641}\sqrt{48+2}$$

Add 48 and 2 to get 50.

$$\frac{24576}{14641}\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{24576}{14641}\times 5\sqrt{2}$$

Express \frac{24576}{14641}\times 5 as a single fraction.

$$\frac{24576\times 5}{14641}\sqrt{2}$$

Multiply 24576 and 5 to get 122880.

$$\frac{122880}{14641}\sqrt{2}$$