Solve (sqrt[4]{3^2})^2

$$( \sqrt[ 4 ] { 3 ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$3$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(\sqrt[4]{9}\right)^{2}$$

Rewrite \sqrt[4]{9} as \sqrt[4]{3^{2}}. Convert from radical to exponential form and cancel out 2 in the exponent. Convert back to radical form.

$$\sqrt[4]{9}=\sqrt[4]{3^{2}}=3^{\frac{2}{4}}=3^{\frac{1}{2}}=\sqrt{3}$$

Insert the obtained value back in the expression.

$$\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3$$

Factor

$$3$$