$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\frac{a^{2}}{b^{3}} .\sqrt{\frac{b^{6}}{a^{4}}} \ ( b >0)\\ A=\sqrt{\frac{\left( a^{2}\right)^{2} .b^{6}}{\left( b^{3}\right)^{2} .a^{4}}}\\ A=\sqrt{\frac{a^{4} .b^{6}}{b^{6} .a^{4}}} =1 \end{array}$