The exponent tells you how many times you multiply a number by itself, and the standard form is the result of the multiplication.

$3^{3}$ would then become $3 · 3 · 3$, and the product of that is $27$.

What would the exponent for $4 · 4 · 4$ be?
What about the product of these numbers?

Repeat the process and complete the rest of the table.