Final answer:
To multiply (4.5 x 10^7) and (3.2 x 10^4), multiply the coefficients to get 14.4, then add the exponents to get 10^11, resulting in 14.4 x 10^11. Adjust the coefficient to fall between 1 and 10, resulting in the final answer of 1.44 x 10^12.
Step-by-step explanation:
The student is asking to perform the multiplication of two numbers expressed in scientific notation: (4.5 × 10^7) (3.2 × 10^4). To solve this, we multiply the decimal parts and then we add the exponents of 10:
- Multiply the coefficients: 4.5 × 3.2 = 14.4
- Add the exponents: The 10^7 multiplied by 10^4 is equal to 10^(7+4), which is 10^11
- Thus, the product of the two numbers is 14.4 × 10^11.
In scientific notation, the coefficient should be a number between 1 and 10, so we adjust the coefficient:
- 14.4 becomes 1.44 when we divide it by 10.
- Since we've divided the coefficient by 10, we need to increase the exponent by 1, making 10^11 become 10^12.
- The final answer in proper scientific notation is: 1.44 × 10^12.