Answer
See the explanation
Work Step by Step
$\begin{array}
AAlgebraic errors&Counterexample\\
(a+b)^2\ne a^2+b^2,&(2+3)^2\ne2^2+3^2\\
\sqrt{a^2+b^2}\ne a+b, &\sqrt{2^2+3^2}\ne 2+3\\
\frac{a+b}{a}\ne b& \frac{2+3}{2}\ne 3\\
\frac{a}{a+b}\ne \frac{1}{b}& \frac{2}{2+3}\ne\frac{1}{3}\\
\frac{a^m}{a^n}\ne a^{m/n}&\frac{5^2}{5^3}\ne5^{2/3}
\end{array}$
