Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{x}^{a}{y}^{2}a}{{x}^{2a-1}}+\frac{{({x}^{2})}^{a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{x}^{a}{y}^{2}a}{{x}^{2a-1}}+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{x}^{a-(2a-1)}{y}^{2}a+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Remove parentheses.
\[{x}^{a-2a+1}{y}^{2}a+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Collect like terms.
\[{x}^{(a-2a)+1}{y}^{2}a+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Simplify \((a-2a)+1\) to \(-a+1\).
\[{x}^{-a+1}{y}^{2}a+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Regroup terms.
\[{x}^{1-a}{y}^{2}a+\frac{{x}^{2a}{y}^{a}}{{x}^{3+a}{y}^{-1}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{x}^{1-a}{y}^{2}a+{x}^{2a-(3+a)}{y}^{a+1}\]
Remove parentheses.
\[{x}^{1-a}{y}^{2}a+{x}^{2a-3-a}{y}^{a+1}\]
Collect like terms.
\[{x}^{1-a}{y}^{2}a+{x}^{(2a-a)-3}{y}^{a+1}\]
Simplify \((2a-a)-3\) to \(a-3\).
\[{x}^{1-a}{y}^{2}a+{x}^{a-3}{y}^{a+1}\]
x^(1-a)*y^2*a+x^(a-3)*y^(a+1)
