5 . Multiply and express the product in scientific notation: $$ \left(4.5 imes 10^{7} ight)\left(3.2 imes 10^{4} ight) $$

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5 . Multiply and express the product in scientific notation: $$ \left(4.5 	imes 10^{7}ight)\left(3.2 	imes 10^{4}ight) $$

UpStudy AI · Accepted Answer

To multiply and express the product of $$ \left(4.5 \times 10^{7}\right) $$ and $$ \left(3.2 \times 10^{4}\right) $$ in scientific notation, follow these steps:

### Step 1: Multiply the Coefficients
Multiply the numerical coefficients (the numbers before the exponents):

$$
4.5 \times 3.2 = 14.4
$$

### Step 2: Add the Exponents
When multiplying powers of 10 with the same base, you add the exponents:

$$
10^{7} \times 10^{4} = 10^{7 + 4} = 10^{11}
$$

### Step 3: Combine the Results
Combine the product of the coefficients with the product of the powers of 10:

$$
14.4 \times 10^{11}
$$

### Step 4: Convert to Proper Scientific Notation
Scientific notation requires the coefficient to be a number between 1 and 10. Since 14.4 is not within this range, adjust it by moving the decimal point one place to the left, which increases the exponent by 1:

$$
14.4 \times 10^{11} = 1.44 \times 10^{1} \times 10^{11} = 1.44 \times 10^{12}
$$

### Final Answer
$$
1.44 \times 10^{12}
$$
The product is $$ 1.44 \times 10^{12} $$.

5 . Multiply and express the product in scientific notation: \( \left(4.5 \times 10^{7}\right)\left(3.2 \times 10^{4}\right) \)

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