(iii) \[\left( \mathbf{a}\text{ }\text{ }\mathbf{b} \right):\text{ }\left( \mathbf{a}\text{ }+\text{ }\mathbf{b} \right),\text{ }{{\left( \mathbf{a}\text{ }+\text{ }\mathbf{b} \right)}^{\mathbf{2}}}:\text{ }({{\mathbf{a}}^{\mathbf{2}}}~+\text{ }{{\mathbf{b}}^{\mathbf{2}}})\text{ }\mathbf{and}\text{ }({{\mathbf{a}}^{\mathbf{4}}}~\text{ }{{\mathbf{b}}^{\mathbf{4}}}):\text{ }{{({{\mathbf{a}}^{\mathbf{2}}}~\text{ }{{\mathbf{b}}^{\mathbf{2}}})}^{\mathbf{2}}}\]
We know that
Compound ratio = \[\left( a\text{ }\text{ }b \right)/\text{ }\left( a\text{ }+\text{ }b \right)\text{ }\times \text{ }{{\left( a\text{ }+\text{ }b \right)}^{2}}/\text{ }({{a}^{2}}~+\text{ }{{b}^{2}})\text{ }\times \text{ }({{a}^{4}}~\text{ }{{b}^{4}})/\text{ }{{({{a}^{2}}~\text{ }{{b}^{2}})}^{2}}\](a – b)/
By further calculation
\[=\text{ }\left( a\text{ }\text{ }b \right)/\text{ }\left( a\text{ }+\text{ }b \right)\text{ }\times \text{ }\left[ \left( a\text{ }+\text{ }b \right)\text{ }\left( a\text{ }+\text{ }b \right) \right]/\text{ }({{a}^{2}}~+\text{ }{{b}^{2}})\text{ }\times \text{ }[({{a}^{2}}~+\text{ }{{b}^{2}})\text{ }\left( a\text{ }+\text{ }b \right)\text{ }\left( a\text{ }\text{ }b \right)\left] /\text{ } \right[{{\left( a\text{ }+\text{ }b \right)}^{2}}~{{\left( a\text{ }\text{ }b \right)}^{2}}]\]
So we get
\[\begin{array}{*{35}{l}}
=\text{ }1/1 \\
=\text{ }1:\text{ }1 \\
\end{array}\]