Exponents are a notation to represent repeated multiplication.
Instead of writing 7·7·7·7·7·7·7·7, we can write this as [tex]7^8[/tex], since there are eight 7's being multiplied together.
In your example, you can rewrite [tex]\dfrac{1}{3}\times\dfrac{1}{3}[/tex] as [tex]\left(\dfrac{1}{3}\right)^2[/tex], since there are two 1/3's being multiplied together.
This should be your first answer for the first blank: [tex]\left(\dfrac{1}{3}\right)^2[/tex]
One note on this is that you will probably need parentheses around your answer: (1/3)^2
Without the parentheses, it changes the meaning, as it changes what's being squared.
The answer for the second blank is the value you get when you multiply [tex]\dfrac{1}{3}\times\dfrac{1}{3}[/tex], which is [tex]\dfrac{1}{9}[/tex].
