###### Exercise37
1. Let $$x^{7}\cdot x^{a}=x^{17}\text{.}$$ Let’s say that $$a$$ is a natural number. How many possibilities are there for $$a\text{?}$$

2. 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 $$b\text{?}$$

3. 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 $$d\text{?}$$

in-context