Question

Expression: (9x10^2) (2x10^3)
Multiply each part:_______x 10^5
Put the first part in scientific notation: (1.8 x ______) x 10^5
Group the powers: 1.8 x (_______)
Combine the powers 1.8 x ________

Answer 1

Do the same thing with (6 x 10 -^4) (4 x 10^7)

Answer 2

Let's multiply the expression step-by-step:

First, we'll multiply the coefficients (the numbers in front) and the powers of ten separately.

1. **Multiply the coefficients**:
\[
9 \times 2 = 18
\]

2. **Add the exponents of 10** (since we are multiplying the powers of ten, we add the exponents):
\[
10^2 \times 10^3 = 10^{2+3} = 10^5
\]

3. **Combine the results**:
Putting it together, we get:
\[
18 \times 10^5
\]

Now, we need to put the coefficient in scientific notation.

4. **Convert 18 to scientific notation**:
\[
18 = 1.8 \times 10^1
\]

5. Now substitute:
\[
1.8 \times 10^1 \times 10^5
\]
This can be rewritten as:
\[
(1.8 \times 10^1) \times 10^5
\]

6. **Group the powers**:
\[
1.8 \times (10^1 \times 10^5)
\]

7. **Combine the powers of ten** (add the exponents):
\[
10^1 \times 10^5 = 10^{1+5} = 10^6
\]

Putting it all together, we have:
\[
1.8 \times 10^6
\]

So, the filled blanks would be as follows:

- Multiply each part: **18 x 10^5**
- Put the first part in scientific notation: **(1.8 x 10^1) x 10^5**
- Group the powers: **1.8 x (10^6)**
- Combine the powers: **1.8 x 10^6**

Answer 3

Let's break down the multiplication of the expression \( (6 \times 10^{-4}) (4 \times 10^{7}) \) step-by-step:

1. **Multiply the coefficients**:
\[
6 \times 4 = 24
\]

2. **Add the exponents of 10**:
\[
10^{-4} \times 10^{7} = 10^{-4 + 7} = 10^{3}
\]

3. **Combine the results**:
Putting it together, we get:
\[
24 \times 10^{3}
\]

Next, we need to put the coefficient in scientific notation.

4. **Convert 24 to scientific notation**:
\[
24 = 2.4 \times 10^{1}
\]

5. Now substitute:
\[
2.4 \times 10^{1} \times 10^{3}
\]
This can be rewritten as:
\[
(2.4 \times 10^{1}) \times 10^{3}
\]

6. **Group the powers**:
\[
2.4 \times (10^{1} \times 10^{3})
\]

7. **Combine the powers of ten** (add the exponents):
\[
10^{1} \times 10^{3} = 10^{1+3} = 10^{4}
\]

Putting it all together, we have:
\[
2.4 \times 10^{4}
\]

So, the filled blanks would be as follows:

- Multiply each part: **24 x 10^{3}**
- Put the first part in scientific notation: **(2.4 x 10^{1}) x 10^{3}**
- Group the powers: **2.4 x (10^{4})**
- Combine the powers: **2.4 x 10^{4}**