Answer
$\frac{1}{27}$
Work Step by Step
When dividing exponential expressions with the same non-zero base, subtract the exponent of the denominator from the exponent of the numerator and give the resulting exponent to the same base:
$$\frac{3^{4}}{3^{7}}$$
$$=3^{(4-7)}$$
$$=3^{(-3)}$$
When an exponential expression has a negative exponent, change the position of the base (from the numerator to the denominator, or vise-versa) and make the exponent positive.
$$=\frac{1}{3^{3}}$$
$$=\frac{1}{27}$$
