\[*\ \cdot a^{7}\ :a^{23} = a^{2}\text{\ \ \ \ }\]
\[*\ \cdot a^{7} = a^{2} \cdot a^{23}\]
\[*\ \cdot a^{7} = a^{25}\]
\[* = a^{25}\ :a^{7}\]
\[*\ = a^{18}.\]