The radical form and exponential form are related by this:
[tex]\sqrt[c]{b}^a=b^{\frac{a}{c}}[/tex]
So, applying this, we will have:
[tex]\sqrt[]{9^3}=\sqrt[2]{9^3}=9^{\frac{3}{2}}[/tex]
However, we can simplify this, because:
[tex]9=3^2[/tex]
So:
[tex]9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}[/tex]
We can use the power to a power rule:
[tex](b^a)^c=b^{a\cdot c}[/tex]
So:
[tex](3^2)^{\frac{3}{2}}=3^{2\cdot\frac{3}{2}}=3^3[/tex]
