Solve [((625)^frac{1{2}})^frac{1{4}}]^2

$$[ ( ( 625 ) ^ { \frac { 1 } { 2 } } ) ^ { \frac { 1 } { 4 } } ] ^ { 2 }$$

Evaluate

$$5$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and \frac{1}{4} to get \frac{1}{8}.

$$\left(625^{\frac{1}{8}}\right)^{2}$$

Use the rules of exponents to simplify the expression.

$$\left(\sqrt[8]{625}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$625^{\frac{1}{8}\times 2}$$

Multiply \frac{1}{8} times 2.

$$\sqrt[4]{625}$$

Raise 625 to the power \frac{1}{4}.

$$5$$

Factor

$$5$$