###### Exercise 37

Let \(x^{7}\cdot x^{a}=x^{17}\text{.}\) Let’s say that \(a\) is a natural number. How many possibilities are there for \(a\text{?}\)

Let \(x^{b}\cdot x^{c}=x^{75}\text{.}\) Let’s say that \(b\) and \(c\) are natural numbers. How many possibilities are there for \(b\text{?}\)

Let \(x^{d}\cdot x^{e}=x^{800}\text{.}\) Let’s say that \(d\) and \(e\) are natural numbers. How many possibilities are there for \(d\text{?}\)