3⁹ is the same as doing:
3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
What I would do it is narrow it down piece by piece.
3 * 3 * 3 = 27. Do that 3 times, now you are left with:
27 * 27 * 27
27 * 27 or 27² = 729.
That leaves you with:
729 * 27
You can multiply by hand or use a calculator to get your answer of 19683.
To check your answer, plug 3⁹ into a calculator. Your answer should match this.