1. **State the problem:** Simplify the expression $x^7 \div x^{10}$ and find which option it equals. 2. **Recall the rule for dividing powers with the same base:** $$a^m \div a^n = a^{m-n}$$ This means when dividing powers with the same base, subtract the exponents. 3. **Apply the rule:** $$x^7 \div x^{10} = x^{7-10} = x^{-3}$$ 4. **Interpret the negative exponent:** A negative exponent means the reciprocal: $$x^{-3} = \frac{1}{x^3}$$ 5. **Compare with the options:** - a. $x^3$ - b. $x^{-3}$ - c. $\frac{1}{x^3}$ - d. $x^{17}$ The expression equals both $x^{-3}$ and $\frac{1}{x^3}$, but the exact simplified form from the division is $x^{-3}$. **Final answer:** $x^{-3}$ (option b)