[tex]E_k=a^4\\
(\sqrt a)^{18-k}\cdot \left(\dfrac{1}{\sqrt[3]{a}}\right)^k=a^4\\
a^{\frac{18-k}{2}}\cdot a^{-\frac{k}{3}}=a^4\\
a^{\frac{18-k}{2}-\frac{k}{3}}=a^4\\
\frac{18-k}{2}-\frac{k}{3}=4|\cdot 6\\
3(18-k)-2k=24\\
54-5k=24\\
5k=30\\
\boxed{k=6}[/tex]
