1. **State the problem:** Factor the expression $x^7$. 2. **Recall the rule:** Any power of a variable can be expressed as the variable multiplied by itself the given number of times. Here, $x^7 = x \times x \times x \times x \times x \times x \times x$. 3. **Factoring:** Since $x^7$ is a single term (a monomial), its factors are $x$ multiplied by itself 7 times. 4. **Final factored form:** $$x^7 = x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x$$ This is the fully factored form over the integers.