1. The problem is to simplify the expression $10^{-4}$. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$. 3. Applying this rule to $10^{-4}$, we get: $$10^{-4} = \frac{1}{10^4}$$ 4. Calculate $10^4$: $$10^4 = 10 \times 10 \times 10 \times 10 = 10000$$ 5. Therefore: $$10^{-4} = \frac{1}{10000} = 0.0001$$ 6. So, the simplified value of $10^{-4}$ is $0.0001$.