Write the equation in exponential form. Assume that all constants are positive and not equal to 1. \[ \log _{25}(5)=\frac{1}{2} \]

Step 1 ：Write the equation in exponential form. Assume that all constants are positive and not equal to 1.

Step 2 ：The given equation is \(\log _{25}(5)=\frac{1}{2}\).

Step 3 ：To convert it to exponential form, we need to remember that the base of the logarithm becomes the base of the exponent, the result of the logarithm becomes the exponent, and the argument of the logarithm becomes the result of the exponentiation.

Step 4 ：So, in this case, the base of the logarithm is 25, the result of the logarithm is 1/2, and the argument of the logarithm is 5.

Step 5 ：Therefore, the equation in exponential form should be \(25^{\frac{1}{2}} = 5\).

Step 6 ：Final Answer: The equation in exponential form is \(\boxed{25^{\frac{1}{2}} = 5}\).