1. **State the problem:** Simplify the expression $2^{100} - 2^{99}$. 2. **Recall the properties of exponents:** For any base $a$ and exponents $m$ and $n$, $a^m - a^n = a^n(a^{m-n} - 1)$ if $m > n$. 3. **Apply the property:** Here, $m=100$ and $n=99$, so $$2^{100} - 2^{99} = 2^{99}(2^{100-99} - 1) = 2^{99}(2^1 - 1).$$ 4. **Simplify inside the parentheses:** $$2^1 - 1 = 2 - 1 = 1.$$ 5. **Final simplification:** $$2^{99} \times 1 = 2^{99}.$$ **Answer:** The simplified form of $2^{100} - 2^{99}$ is $2^{99}$.