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

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

Evaluate

$$2$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

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

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

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

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

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

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

$$\sqrt{\frac{8}{2}}$$

Divide 8 by 2 to get 4.

$$\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2$$

Factor

$$2$$