The image contains two problems where you are asked to find the product and write the expression in both scientific and expanded form. Let’s go through each one step by step.

1. First Expression:

$(2 \times 10^5) \times (4 \times 10^2)$

To solve this:

• Multiply the numbers $2 \times 4 = 8$.
• For the powers of 10, add the exponents $5 + 2 = 7$.

Thus, the product in scientific form is:

$8 \times 10^7$

In expanded form, this would be:

$8 \times 10,000,000 = 80,000,000$

2. Second Expression:

$(3 \times 10^4) \times (3 \times 10^{-2})$

To solve this:

• Multiply the numbers $3 \times 3 = 9$.
• For the powers of 10, add the exponents $4 + (-2) = 2$.

Thus, the product in scientific form is:

$9 \times 10^2$

In expanded form, this would be:

$9 \times 100 = 900$

Would you like further details on how scientific notation works, or have any questions about this?

Related Questions:

1. How do you multiply numbers in scientific notation in general?
2. How do you convert scientific notation into standard form?
3. Can you explain how exponents are added when multiplying powers of ten?
4. How does the negative exponent affect the result in the second expression?
5. What are some other examples of multiplying numbers in scientific notation?

Tip:

When multiplying numbers in scientific notation, always remember to multiply the base numbers and add the exponents of 10!