Expression: (9x10^2) (2x10^3)

Question

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

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 2

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

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}