Calculate the average rate of change of $f(x)=\frac{1}{\sqrt{x}}$ on $[1,49]$.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)

Step 1 ：The function given is \(f(x) = \frac{1}{\sqrt{x}}\).

Step 2 ：We are asked to find the average rate of change of this function on the interval \([1, 49]\).

Step 3 ：The formula for the average rate of change of a function \(f(x)\) on the interval \([a, b]\) is \(\frac{f(b) - f(a)}{b - a}\).

Step 4 ：Substituting the given values into the formula, we get \(\frac{f(49) - f(1)}{49 - 1}\).

Step 5 ：Solving this, we find that \(f(49) = \frac{1}{\sqrt{49}} = \frac{1}{7}\) and \(f(1) = \frac{1}{\sqrt{1}} = 1\).

Step 6 ：Substituting these values back into the formula, we get \(\frac{\frac{1}{7} - 1}{49 - 1} = \frac{-\frac{6}{7}}{48}\).

Step 7 ：Simplifying this, we find that the average rate of change of the function \(f(x) = \frac{1}{\sqrt{x}}\) on the interval \([1, 49]\) is \(-\frac{1}{56}\).

Step 8 ：\(\boxed{-\frac{1}{56}}\) is the final answer.