Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sqrt[x}+\frac{1}{y]{n}=\sqrt[xy]{n}\]
Cancel the base of \(n\) on both sides.
\[\frac{1}{x}+\frac{1}{y}=\frac{1}{xy}\]
Multiply both sides by \(xy\).
\[(\frac{1}{x}+\frac{1}{y})xy=1\]
Regroup terms.
\[xy(\frac{1}{x}+\frac{1}{y})=1\]
Expand.
\[y+x=1\]
Subtract \(x\) from both sides.
\[y=1-x\]
y=1-x
