Solve sqrt{2^9^4^-2^-1}

$$\sqrt { 2 ^ { 9 ^ { 4 ^ { - 2 ^ { - 1 } } } } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\sqrt{2^{9^{4^{-\frac{1}{2}}}}}$$

Calculate 4 to the power of -\frac{1}{2} and get \frac{1}{2}.

$$\sqrt{2^{9^{\frac{1}{2}}}}$$

Calculate 9 to the power of \frac{1}{2} and get 3.

$$\sqrt{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}$$