Can fractions be written as another fraction with a particular denominator?

Question

Suppose we have a fraction $0 < \frac{a}{b} \leq 1$, where $a, b \in \mathbb{Q}, b \neq 0$. Can this fraction be written with another base in its denominator? Say I want to express this fraction with a denominator that its base is $3$. So the new denominator would be $3^n$ for some $n \in \mathbb{N}.$ Then can we find $c$ such that $\frac{a}{b} = \frac{c}{3^n}$ and $c \in \mathbb{N}$? For a concrete example, let $\frac{7}{10}$. How do we one find $n$ and $c$ such that $\frac{c}{3^n} = \frac{7}{10}?$