1. **State the problem:** Simplify the expression $$\frac{(0.0003 \times 10^{-8})(8000 \times 10^{6})}{0.004 \times 10^{5}}$$. 2. **Rewrite the numbers in scientific notation:** $$0.0003 = 3 \times 10^{-4}$$ $$8000 = 8 \times 10^{3}$$ $$0.004 = 4 \times 10^{-3}$$ 3. **Substitute these into the expression:** $$\frac{(3 \times 10^{-4} \times 10^{-8})(8 \times 10^{3} \times 10^{6})}{4 \times 10^{-3} \times 10^{5}}$$ 4. **Combine powers of 10:** $$\frac{(3 \times 10^{-4-8})(8 \times 10^{3+6})}{4 \times 10^{-3+5}} = \frac{(3 \times 10^{-12})(8 \times 10^{9})}{4 \times 10^{2}}$$ 5. **Multiply the numerators:** $$3 \times 8 = 24$$ $$10^{-12} \times 10^{9} = 10^{-3}$$ So numerator is $$24 \times 10^{-3}$$ 6. **Write the entire fraction:** $$\frac{24 \times 10^{-3}}{4 \times 10^{2}}$$ 7. **Divide the coefficients:** $$\frac{24}{4} = 6$$ 8. **Divide the powers of 10:** $$10^{-3} \div 10^{2} = 10^{-3-2} = 10^{-5}$$ 9. **Combine results:** $$6 \times 10^{-5}$$ 10. **Final answer:** $$6 \times 10^{-5}$$