A physical quantity \(P\) is related to four observables \(a\), \(b\), \(c\), and \(d\) as
\[
P=\frac{\sqrt{ab}\cdot d^{\alpha}}{\sqrt{c}}
\]
(\(\alpha\) is a constant). The percentage errors in \(a\), \(b\), \(c\), and \(d\) are \(0.5\%\) each. If the percentage error in \(P\) is \(2\%\), then \(\alpha\) is