Find the value of x in log

Question

If $\log_{\sqrt 8} \,⁡x=\frac {10}3$, then find the value of $x$. I get the intermediate step of $2 ^ {10/9}$ but in the answers it says $2^5$. How?

Answer 1

$$\begin{array}{rcl} \log_{\sqrt8}x &=& \dfrac{10}3 \\ x &=& \sqrt{8}^{10/3} \\ x &=& (\sqrt{2^3})^{10/3} \\ x &=& (2^{3/2})^{10/3} \\ x &=& 2^5 \\ \end{array}$$