Let’s break down each expression and find the answer for all the multiplication problems involving scientific notation:

1. $(2 \times 10^3)(5 \times 10^3)$
   • Multiply the coefficients: $2 \times 5 = 10$
   • Add the exponents: $10^3 \times 10^3 = 10^{3+3} = 10^6$
   • Answer: $10 \times 10^6 = 1.0 \times 10^7$

2. $(9 \times 10^2)(8 \times 10^6)$
   • Multiply the coefficients: $9 \times 8 = 72$
   • Add the exponents: $10^2 \times 10^6 = 10^{2+6} = 10^8$
   • Answer: $72 \times 10^8 = 7.2 \times 10^9$

3. $(1 \times 10^{-5})(2 \times 10^{-9})$
   • Multiply the coefficients: $1 \times 2 = 2$
   • Add the exponents: $10^{-5} \times 10^{-9} = 10^{-5+(-9)} = 10^{-14}$
   • Answer: $2 \times 10^{-14}$

4. $(4 \times 10^7)(2 \times 10^3)$
   • Multiply the coefficients: $4 \times 2 = 8$
   • Add the exponents: $10^7 \times 10^3 = 10^{7+3} = 10^{10}$
   • Answer: $8 \times 10^{10}$

5. $(9 \times 10^{-3})(5 \times 10^{-5})$
   • Multiply the coefficients: $9 \times 5 = 45$
   • Add the exponents: $10^{-3} \times 10^{-5} = 10^{-8}$
   • Answer: $45 \times 10^{-8} = 4.5 \times 10^{-7}$

6. $(7 \times 10^8)(4 \times 10^6)$
   • Multiply the coefficients: $7 \times 4 = 28$
   • Add the exponents: $10^8 \times 10^6 = 10^{8+6} = 10^{14}$
   • Answer: $28 \times 10^{14} = 2.8 \times 10^{15}$

Summary of Answers:

1. $1.0 \times 10^7$
2. $7.2 \times 10^9$
3. $2 \times 10^{-14}$
4. $8 \times 10^{10}$
5. $4.5 \times 10^{-7}$
6. $2.8 \times 10^{15}$

Would you like a detailed explanation of any specific step? 😊 Here are some related questions to expand on this topic:

1. What are the rules for multiplying numbers in scientific notation?
2. How do you convert large or small numbers into scientific notation?
3. What happens when the coefficient exceeds 10 in scientific notation?
4. Can scientific notation be used in addition and subtraction?
5. How is scientific notation applied in real-life scientific measurements?

Tip: When multiplying in scientific notation, always combine the coefficients first and then apply the exponent rules.