Question

what do the positive exponents tell you about the factors?
when the base is 3, a positive exponent tells
the number of times 3 is used as
a factor.
what do the negative exponents tell you about
the factors?
when the base is 3, a negative exponent
tells the number of times ? is used as
a factor.
$3^n$ valu
$3^3$ 27
$3^2$ 9
$3^1$ 3
$3^0$ 1
$3^{-1}$ $\frac{1}{3}$
$3^{-2}$ $\frac{1}{9}$
$3^{-3}$ $\frac{1}{27}$

Explanation:

Negative exponents represent the reciprocal of the base raised to the positive version of that exponent. For base 3, a negative exponent means we use the reciprocal of 3, which is $\frac{1}{3}$, as a factor the number of times equal to the positive value of the exponent. This matches the table values: $3^{-1}=\frac{1}{3}$, $3^{-2}=\frac{1}{3} \times \frac{1}{3}$, etc.

Answer:

$\frac{1}{3}$