Answer
$$\frac{1}{g^{4}}$$
Work Step by Step
To multiply powers of the same base, add the exponents. An expression raised to a negative power is equal to the reciprocal of that expression raised to the same positive power:
$$g^{-3}g^{-1}=g^{(-3)+(-1)}=g^{-4}=\frac{1}{g^{4}}.$$
