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

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

Evaluate

$$\sqrt{5}\approx 2.236067977$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(625^{-\frac{1}{2}}\right)^{-\frac{1}{4}}$$

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

$$625^{-\frac{1}{2}\left(-\frac{1}{4}\right)}$$

Multiply -\frac{1}{2} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\sqrt[8]{625}$$

Raise 625 to the power \frac{1}{8}.

$$\sqrt{5}$$