Solve $\sqrt{3}^n=3^3$ I got answer but i could not understand, can anyone explain me ?
$\sqrt{3}^n=3^3$
$\implies{3}^{n/2}=3^3$
$\implies \frac{n}{2}=3\implies n=6$
How we get ${3}^{n/2}$ in the second line and how we get $\frac{n}{2}$ in third line.

$$\sqrt{x} = x^{\frac{1}{2}}$$
Since if $\sqrt{x}\sqrt{x} = x$ by definition then it follows that $x^kx^k = x^1$ where $2k = 1$ so $k = \frac{1}{2}$. If you choose to agree with this, then
$$\sqrt{3^n} = \sqrt{3}^\frac{n}{2} = 3^3  \implies \frac{n}{2} = 3 \implies n = 6$$
