1. **State the problem:** We need to simplify the expression $$\frac{3 \times 10^{-2}}{8 \times 10^{-1}}$$ and understand how to divide exponents. 2. **Recall the rule for dividing powers with the same base:** When dividing terms with the same base, subtract the exponents: $$a^m \div a^n = a^{m-n}$$ 3. **Apply this rule to the powers of 10:** $$10^{-2} \div 10^{-1} = 10^{-2 - (-1)} = 10^{-2 + 1} = 10^{-1}$$ 4. **Divide the coefficients (numbers in front):** $$\frac{3}{8} = 0.375$$ 5. **Combine the results:** $$\frac{3 \times 10^{-2}}{8 \times 10^{-1}} = 0.375 \times 10^{-1}$$ 6. **Express the final answer in standard scientific notation:** $$0.375 \times 10^{-1} = 3.75 \times 10^{-2}$$ **Final answer:** $$3.75 \times 10^{-2}$$