1. **State the problem:** Multiply the numbers in scientific notation: $$(7.7 \times 10^{-3}) (3 \times 10^{-5})$$ 2. **Recall the multiplication rule for scientific notation:** When multiplying numbers in scientific notation, multiply the coefficients and add the exponents of 10. 3. **Multiply the coefficients:** $$7.7 \times 3 = 23.1$$ 4. **Add the exponents:** $$-3 + (-5) = -8$$ 5. **Combine the results:** $$23.1 \times 10^{-8}$$ 6. **Express in proper scientific notation:** Since 23.1 is greater than 10, rewrite as $$2.31 \times 10^{1}$$ and multiply by $$10^{-8}$$: $$2.31 \times 10^{1} \times 10^{-8} = 2.31 \times 10^{-7}$$ **Final answer:** $$2.31 \times 10^{-7}$$