1. The problem is to understand and simplify the expression $7^{-5}$. 2. The rule for negative exponents states that $a^{-n} = \frac{1}{a^n}$ where $a$ is a nonzero number and $n$ is a positive integer. This means a negative exponent indicates the reciprocal of the base raised to the positive exponent. 3. Applying this rule to $7^{-5}$, we get: $$7^{-5} = \frac{1}{7^5}$$ 4. This shows that $7^{-5}$ is the same as one divided by $7$ raised to the fifth power. 5. To understand $7^5$, it means multiplying 7 by itself 5 times: $$7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16807$$ 6. Therefore, the simplified value of $7^{-5}$ is: $$7^{-5} = \frac{1}{16807}$$ This is the final answer, showing the negative exponent converted into a fraction with a positive exponent in the denominator.