Solve sqrt{2^(sqrt[3]{(frac{1{2})^3^2})^-1}}

$$\sqrt { 2 ^ { ( \sqrt[ 3 ] { ( \frac { 1 } { 2 } ) ^ { 3 ^ { 2 } } } ) ^ { - 1 } } }$$

Evaluate

$$16$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\sqrt{2^{\left(\sqrt[3]{\left(\frac{1}{2}\right)^{9}}\right)^{-1}}}$$

Calculate \frac{1}{2} to the power of 9 and get \frac{1}{512}.

$$\sqrt{2^{\left(\sqrt[3]{\frac{1}{512}}\right)^{-1}}}$$

Calculate \sqrt[3]{\frac{1}{512}} and get \frac{1}{8}.

$$\sqrt{2^{\left(\frac{1}{8}\right)^{-1}}}$$

Calculate \frac{1}{8} to the power of -1 and get 8.

$$\sqrt{2^{8}}$$

Calculate 2 to the power of 8 and get 256.

$$\sqrt{256}$$

Calculate the square root of 256 and get 16.

$$16$$

Factor

$$2^{4}$$