A physical quantity ' X ' is related to four measurable quantities ' a ', ' b ', ' c ' and ' d ' as…

The percentage error in $X = a^p b^q c^r d^s$ is given by:

$\frac{\Delta X}{X} \times 100 = |p| \frac{\Delta a}{a} \times 100 + |q| \frac{\Delta b}{b} \times 100 + |r| \frac{\Delta c}{c} \times 100 + |s| \frac{\Delta d}{d} \times 100$

For $X = a^2 b^3 c^{5/2} d^{-2}$ with percentage errors of $1\%$, $2\%$, $2\%$, and $4\%$ respectively:

$\frac{\Delta X}{X} \times 100 = |2|(1\%) + |3|(2\%) + |5/2|(2\%) + |-2|(4\%) = 2\% + 6\% + 5\% + 8\% = 21\%$

The percentage error in $X$ is $21\%$.