 Second-order relative change of a monomial

For positive $a,b$, fixed real $p,q$, and $f(a,b)=a^p{b}^q$, change the inputs to $a(1+h),b(1+j)$ with $h,j$ small. The ratio of the new value to the old one is exactly $(1+h{)}^p(1+j{)}^q$. Applying the binomial series to each factor and multiplying proves the displayed Taylor expansion. Positive inputs and $1+h,1+j>0$ make arbitrary real exponents well defined. A percentage change of $k$ in $a$ means $h=k/100$, not $h=k$. The mixed term $pqhj$ is required even though there is no such term in either one-variable expansion separately.