1. **State the problem:** Evaluate the product of two numbers in scientific notation: $$(7.7 \times 10^{-3})(3 \times 10^{-5})$$ 2. **Recall the exponential rule:** When multiplying numbers in scientific notation, multiply the decimal parts and add the exponents of 10: $$a \times 10^m \times b \times 10^n = (a \times b) \times 10^{m+n}$$ 3. **Apply the rule:** $$7.7 \times 3 = 23.1$$ $$10^{-3} \times 10^{-5} = 10^{-3 + (-5)} = 10^{-8}$$ 4. **Combine the results:** $$(7.7 \times 10^{-3})(3 \times 10^{-5}) = 23.1 \times 10^{-8}$$ 5. **Convert to standard notation:** Since $23.1$ is not between 1 and 10, rewrite it as: $$23.1 = 2.31 \times 10^1$$ 6. **Substitute back:** $$23.1 \times 10^{-8} = (2.31 \times 10^1) \times 10^{-8} = 2.31 \times 10^{1-8} = 2.31 \times 10^{-7}$$ 7. **Final answer in standard notation:** $$2.31 \times 10^{-7}$$