$解:{a}^{9}=a·{a}^{8}={a}^{2}·{a}^{7}={a}^{3}·{a}^{6}={a}^{4}·{a}^{5}$
$有4种写法$
${a}^{9}={a}^{1}·{a}^{1}·{a}^{7}={a}^{1}·{a}^{2}·{a}^{6}={a}^{1}·{a}^{3}·{a}^{5}={a}^{1}·{a}^{4}·{a}^{4}={a}^{2}·{a}^{2}·{a}^{5}={a}^{2}·{a}^{3}·{a}^{4}={a}^{3}·{a}^{3}·{a}^{3}$
$有7种写法$